Mathematics: What is the measure of arc KL?

What is the measure of arc KL?, №13299651, 13.05.2022 23:57

Mathematics

For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with chords JK and LM intersecting at N inside the circle 1 7 9 4 Question 7(Multiple Choice Worth 1 points) (07.01 MC) Lines CD and DE are tangent to circle A: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 112 degrees. Point B lies on circle A. If arc CE is 112°, what is the measure of ∠CDE? 124° 136° 68° 56° Question 8(Multiple Choice Worth 1 points) (07.01 MC) Lines CD and CE are tangent to circle a. If m∠DAE = 140°, what is the measure

Step-by-step answer

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Question set:

Question 6 For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with chords JK and LM intersecting at N inside the circle 1 7 9 4

Question 7(Multiple Choice Worth 1 points) (07.01 MC) Lines CD and DE are tangent to circle A: Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 112 degrees. Point B lies on circle A. If arc CE is 112°, what is the measure of ∠CDE? 124° 136° 68° 56°

Question 8(Multiple Choice Worth 1 points) (07.01 MC) Lines CD and CE are tangent to circle a. If m∠DAE = 140°, what is the measure of ∠DCE? Tangent CD intersects with circle A at point D, tangent CE intersects with circle A at point E, angle ECD is on the exterior of circle A, and angle DAE has a vertex on the center of circle A. 80° 140° 40° 220°

Question 9(Multiple Choice Worth 1 points) (07.01 MC) Find the measure of arc EC. Circle A with chords EF and CD that intersect at point G, the measure of arc EC is 5x degrees, the measure of angle EGC is 7x degrees, and the measure of arc DF is 90 degrees. 50° 70° 100° 140°

Question 10(Multiple Choice Worth 1 points) (07.01 MC) In circle A, marc BC is 67° and marc EF is 74°: Points B, C, E, and F lie on Circle A. Lines BE and CF pass through point D, creating angle EDF. The measure of arc BC is 67 degrees, and the measure of arc EF is 74 degrees. What is m∠FDE? 37° 74° 70.5° 33.5°

Answer set:

Q. 6

Options:

a. 1

b. 7

c. 9

d. 4

Answer:

c. 9

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

Question set:Question 6 For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with ----> by intersecting chords theorem

substitute the given values

Question set:Question 6 For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with

solve for x

Question set:Question 6 For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with

Q. 7

Options:

a 124°

b 136°

c 68°

d 56°

Answer:

c 68°

Explanation:

The measure of ∠CDE is 68degrees

This question bothers on circle geometry;

From the diagram, we can see that ACDE will form a quadrilateral. Since the sum of angles of a quadrilateral is 360degrees, hence;

Question set:Question 6 For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with

From the diagram, since CD and DE are both tangential to the circle at point C and E, this shows that <E = <E = 90°

substituting the given values in the formula;

Question set:Question 6 For circle H, JN = x, NK = 2, LN = 3, and NM = 6. Solve for x. circle H with

Hence the measure of ∠CDE is 68 degrees

Q. 8

Options:

A - 80°
B - 140°
C - 40°
D - 220°

Answer:

C - 40°

Step-by-step explanation:

From the figure we can see a circle.

CD and CE are the two tangents from a common external point C.

CD = CE

To find the measure of <DCE

Consider the quadrilateral <DAE.

<D = <E = 90° [ Angles made with tangent and radius]

m<DCE + m<DAE = 180°

m<DCE = 180- m<DAE

= 180 - 140

= 40°

The correct answer is option C - 40°

Q. 9

Options:

a. 50°

b. 70°

c. 100°

d. 140°

Answer:

b. 70°

Explanation:

m∠EGC=70°

Step-by-step explanation:

we know that

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

m∠EGC=(1/2)[arc EC+arc DF]

Find the value of x

we have

m∠EGC=(7x+7)°

arc EC=50°

arc DF=10x°

substitute and solve for x

(7x+7)°=(1/2)[50°+10x°]

14x+14=50+10x

14x-10x=50-14

4x=36

x=9

Find the measure of angle EGC

m∠EGC=(7x+7)°

substitute the value of x

m∠EGC=(7(9)+7)°=70°

Q. 10

Options:

a. 37°
b. 74°
c. 70.5°
d. 33.5°

Answer:

c. 70.5°
Explanation:

So here is how we find the measurement of m∡FDE. Given that mArc BC is 67° and mArc EF is 74°.
<fde=1/2∗(67+74)
<fde = 1/2*(141)
<fde = 70.5
Therefore, the measurement of m∡FDE is 70.5° and that would be the third option. Hope this is the answer that you are looking for.

Mathematics

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Circle C is shown. Line segments E C and D F are radii. Lines are drawn from points E and D to point F to form chords E F and D F. Tangents E G and D G intersect at point G outside of the circle. Angle E G D is 60 degrees and angles G E C and G D C are right angles. The lengths of E F and D F are congruent. Which statements about the arcs and angles are true? Select three options. ∠EFD ≅ ∠EGD ∠EGD ≅ ∠ECD Arc E D is-congruent-to arc

Step-by-step answer

P Answered by PhD

99

The relationship between the angles formed in a circle are described by

circle theorems.

The true statements are;

m∠EFD ≅ m∠EGD $\overline{ED}$ ≅ $\overline{FD}$ $m\widehat{FD}$ = 120°

Reasons:

According to the outside angle theorem, we have;

$\displaystyle m\angle EGD = \frac{m\widehat{EFD} - m\widehat{ED}}{2}$

Therefore;

2 × m∠EGD = $m\widehat{EFD} - m\widehat{ED}$

2 × 60° = 120° = $m\widehat{EFD} - m\widehat{ED}$

$m\widehat{EFD} + m\widehat{ED}$ = 360° sum of angles formed at the center of the circle

$m\widehat{ED}$ = 360° - $\mathbf{m\widehat{EFD}}$

120° = $\mathbf{m\widehat{EFD} - m\widehat{ED}}$

120° = $m\widehat{EFD}$ - (360° -

120° = 2· $m\widehat{EFD}$ - 360°

$\displaystyle \frac{120^{\circ}}{2} = \mathbf{\frac{2 \cdot m\widehat{EFD} - 360^{\circ}}{2}}$

Which gives;

60° = $m\widehat{EFD}$ - 180°

$m\widehat{EFD}$ = 60° + 180° = 240°

$m\widehat{EFD}$ = 240°

$m\widehat{ED}$ = 360° - $m\widehat{EFD}$ = 360° - 240° = 120°

$m\widehat{ED}$ = 120°

$m\widehat{ED}$ = 2 × m∠EFD angle subtended by an arc at the center is twice the angle subtended at the circumference

∴ $m\widehat{ED}$ = 120° = 2 × m∠EFD

$\displaystyle m\angle EFD = \frac{120^{\circ}}{2} = 60^{\circ}$

Therefore;

m∠EFD = m∠EGD = m∠G = 60°

m∠EGD = 60°

m∠EFD ≅ m∠EGD by definition of congruency

$m\widehat{ED}$ = m∠ECD by definition of the measure of an arc

∴ $m\widehat{ED}$ = 120° = m∠ECD

∴ m∠ECD ≠ m∠EGD = 60°

m∠ECD $\ncong$ m∠EGD

Given that m∠EFD = 60°, and ΔEFD is an isosceles triangle, we have;

∠DEF = ∠FDE

∠DEF + ∠FDE = 180° - 60° = 120°

∴ ∠DEF = ∠FDE = 60°

Therefore;

ΔEFD is an equilateral triangle (all angles are equal to 60°)

$\widehat{ED}$ = $\widehat{FD}$ Equal chord subtend equal minor arcs theorem

Therefore;

$\underline{\overline{ED} \cong \overline{FD}}$ by definition of congruency

$\widehat{ED}$ = 120° = $\widehat{FD}$

∴ $\underline{\widehat{FD} = 120^{\circ}}$

Learn more about circle theorems here:

link

Mathematics

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Circle C is shown. Line segments E C and D F are radii. Lines are drawn from points E and D to point F to form chords E F and D F. Tangents E G and D G intersect at point G outside of the circle. Angle E G D is 60 degrees and angles G E C and G D C are right angles. The lengths of E F and D F are congruent. Which statements about the arcs and angles are true? Select three options. ∠EFD ≅ ∠EGD ∠EGD ≅ ∠ECD Arc E D is-congruent-to arc

Step-by-step answer

P Answered by PhD

39

∠EFD ≅ ∠EGD Arc E D is-congruent-to arc F D mArc F D = 120°

Step-by-step explanation:

In Quadrilateral GECD,

$60^0+90^0+90^0+ \angle ECD=360^0\angle ECD=360^0-240^0=120^0\\\angle EFD=\frac{1}{2} \angle ECD \text{ (Inscribed Angle Theorem)}\\\angle EFD =\frac{1}{2} X 120 =60^0\\Therefore: \angle EFD=\angle EGD$

In Triangle EFD,

$\angle FED =\angle FDE \text{ (base angles of an isosceles triangle)}\\\angle FED +\angle FDE+\angle EFD=180^0\\\angle FED +\angle FDE+60=180\\\angle FED +\angle FDE=120\\\angle FED =\angle FDE=60^0$

Similarly, In Triangle GED

$\angle GED =\angle GDE \text{ (tangent to a circle)}\\\angle GED +\angle GDE+\angle EGD=180^0\\\angle GED +\angle GDE+60=180\\\angle GED +\angle GDE=120\\\angle GED =\angle GDE=60^0\\Therefore, mArc F D = 120\°$

Finally, Arc ED is-congruent-to arc F D

The first, third and last options are true.

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measu

Mathematics

Points E, F, and D are on circle C, and angle G measures 60°. The measure of arc EF equals the measure of arc FD. Circle C is shown. Line segments E C and D F are radii. Lines are drawn from points E and D to point F to form chords E F and D F. Tangents E G and D G intersect at point G outside of the circle. Angle E G D is 60 degrees and angles G E C and G D C are right angles. The lengths of E F and D F are congruent. Which statements about the arcs and angles are true? Select three options. ∠EFD ≅ ∠EGD ∠EGD ≅ ∠ECD Arc E D is-congruent-to arc

Step-by-step answer

P Answered by PhD

39

∠EFD ≅ ∠EGD Arc E D is-congruent-to arc F D mArc F D = 120°

Step-by-step explanation:

In Quadrilateral GECD,

$60^0+90^0+90^0+ \angle ECD=360^0\angle ECD=360^0-240^0=120^0\\\angle EFD=\frac{1}{2} \angle ECD \text{ (Inscribed Angle Theorem)}\\\angle EFD =\frac{1}{2} X 120 =60^0\\Therefore: \angle EFD=\angle EGD$

In Triangle EFD,

$\angle FED =\angle FDE \text{ (base angles of an isosceles triangle)}\\\angle FED +\angle FDE+\angle EFD=180^0\\\angle FED +\angle FDE+60=180\\\angle FED +\angle FDE=120\\\angle FED =\angle FDE=60^0$

Similarly, In Triangle GED

$\angle GED =\angle GDE \text{ (tangent to a circle)}\\\angle GED +\angle GDE+\angle EGD=180^0\\\angle GED +\angle GDE+60=180\\\angle GED +\angle GDE=120\\\angle GED =\angle GDE=60^0\\Therefore, mArc F D = 120\°$

Finally, Arc ED is-congruent-to arc F D

The first, third and last options are true.

Mathematics

Given: circle o; angle a intercepts arc b c d ; angle d intercepts arc b c prove: angle a is-congruent-to angle d circle o is shown. angles a and d intercept arc b c. angles b and c intercept arc a d. two statements are missing reasons. what reason can be used to justify both statements 2 and 3? statements reasons 1. circle o; angle a intercepts arc b c. angle d intercects arc b c 1. given 2. measure of angle a = one-half (measure of arc b c) 2. ? 3. measure of angle d = one-half (measure of arc b c) 3. ? 4. measure of angle a = measure of angle

Step-by-step answer

P Answered by Specialist

87

A. Inscribed angles theorem

Step-by-step explanation:

A.inscribed angles theorem

B.third corollary to the inscribed angles theorem

C.central angle of a triangle has the same measure as its intercepted arc.

D.Angle formed by a tangent and a chord is half the measure of the intercepted arc.

Just took the unit test on edgen and got 100

Mathematics

Given: circle o; angle a intercepts arc b c d ; angle d intercepts arc b c prove: angle a is-congruent-to angle d circle o is shown. angles a and d intercept arc b c. angles b and c intercept arc a d. two statements are missing reasons. what reason can be used to justify both statements 2 and 3? statements reasons 1. circle o; angle a intercepts arc b c. angle d intercects arc b c 1. given 2. measure of angle a = one-half (measure of arc b c) 2. ? 3. measure of angle d = one-half (measure of arc b c) 3. ? 4. measure of angle a = measure of angle

Step-by-step answer

P Answered by Specialist

87

A. Inscribed angles theorem

Step-by-step explanation:

A.inscribed angles theorem

B.third corollary to the inscribed angles theorem

C.central angle of a triangle has the same measure as its intercepted arc.

D.Angle formed by a tangent and a chord is half the measure of the intercepted arc.

Just took the unit test on edgen and got 100

Mathematics

Use the information given in the diagram to prove that m∠JGI = One-half(b – a), where a and b represent the degree measures of arcs FH and JI. A circle is shown. Secants G J and G I intersect at point G outside of the circle. Secant G J intersects the circle at point F. Secant G I intersects the circle at point H. The measure of arc F H is a. The measure of arc J I is b. A dotted line is drawn from point J to point H. Angles JHI and GJH are inscribed angles. We have that m∠JHI = One-half b and m∠GJH = One-halfa by the . Angle JHI is an exterior

Step-by-step answer

P Answered by Specialist

6

inscribed angle theorem, gjh, substitution property

Mathematics

Circle D is shown with the measures of the minor arcs. Circle D is shown. Line segments D E, D F, D G, and D H are radii. Lines are drawn to connect the points on the circle and to create secants E F, F G, G H, and H E. The measure of arc E F is 115 degrees, the measure of arc F G is 115 degrees, the measure of arc G H is 65 degrees, and the measure of arc H E is 65 degrees. Which segments are congruent? EH and EF GH and FE FG and EH EF and GF

Step-by-step answer

P Answered by Specialist

Options:

a. <EDH and <EDF
b. <EDF and <FDG
c. <FDG and <GDH
d. <GDH and <EDF

Answer:

b. <EDF and <FDG

Step-by-step explanation:

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

They have the same shape and size and angles. Also you can see that they are symmetric.

Options:a. <EDH and <EDFb. <EDF and <FDGc. <FDG and <GDHd. <GDH and <EDFAns

Mathematics

Geometry problem. i don t understand this question! the diameter ac of circle o is 24 cm. arcs ab and cd are congruent. angle doc = 60° use this information, the diagram, and your rules for chords, arcs and angles in circles from unit 4 to solve the questions below. explain your reasoning for each answer to get full credit. each one is worth 3 points. measure of arc dc = measure of arc ab = measure of angle acb = measure of angle aod = measure of angle abc = measure of arc bc =

Step-by-step answer

P Answered by PhD

14

A. $\text{Measure of arc DC}=60^o$

B. $\text{Measure of arc AB}=60^o$

C. $m\angle ACB=30^o$

D. $m\angle AOD=120^o$

E. $m\angle ABC=90^o$

F. $\text{Measure of Arc BC}=120^o$

Step-by-step explanation:

We have been given that the diameter AC of circle O is 24 cm. Arcs AB and CD are congruent. Angle DOC = 60° .

A. Since we know that the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.

We can see that angle DOC is central angle and $m\angle DOC=60^o$ and arc DC subtends to central angle, therefore, the measure of arc DC will be 60 degrees.

B. Since we are told that arcs AB and CD are congruent and measure of arc DC is 60 degrees, therefore, measure of arc AB will be 60 degrees as well.

C. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Measure of Arc AB is 60 degrees, so by inscribed angle theorem the measure of angle ACB will be half the measure of AB.

$m\angle ACB=\frac{1}{2}\times \text{The measure of arc AB}$

$m\angle ACB=\frac{1}{2}\times 60^o$

$m\angle ACB=30^o$

Therefore, measure of angle ACB will be 30 degrees.

D. We can see that angle DOC and AOD form a linear pair of angles, so they will add up-to 180 degrees.

$m\angle DOC+m\angle AOD=180^o$

Upon substituting measure of angle DOC we will get,

$60^o+m\angle AOD=180^o$

$60^o-60^o+m\angle AOD=180^o-60^o$

$m\angle AOD=120^o$

Therefore, measure of angle AOD will be 120 degrees.

E. Since we know that angle inscribed in a semicircle is always a right angle. We can see that angle ABC is angle inscribed in the semicircle as AC is the diameter of our given circle, therefore, measure of angle ABC will be 90 degrees.

F. Since we know that arc measure of a semicircle is 180 degrees. We can see that arc ABC is arc of the semicircle, so we can set an equation as:

$\text{Measure of arc AB+ Measure of Arc BC}=180^o$

Upon substituting measure of arc AB we will get,

$60^o+\text{Measure of Arc BC}=180^o$

$60^o-60^o+\text{Measure of Arc BC}=180^o-60^o$

$\text{Measure of Arc BC}=120^o$

Therefore, measure of arc BC is 120 degrees.

Mathematics

Geometry problem. i don t understand this question! the diameter ac of circle o is 24 cm. arcs ab and cd are congruent. angle doc = 60° use this information, the diagram, and your rules for chords, arcs and angles in circles from unit 4 to solve the questions below. explain your reasoning for each answer to get full credit. each one is worth 3 points. measure of arc dc = measure of arc ab = measure of angle acb = measure of angle aod = measure of angle abc = measure of arc bc =

Step-by-step answer

P Answered by PhD

14

A. $\text{Measure of arc DC}=60^o$

B. $\text{Measure of arc AB}=60^o$

C. $m\angle ACB=30^o$

D. $m\angle AOD=120^o$

E. $m\angle ABC=90^o$

F. $\text{Measure of Arc BC}=120^o$

Step-by-step explanation:

We have been given that the diameter AC of circle O is 24 cm. Arcs AB and CD are congruent. Angle DOC = 60° .

A. Since we know that the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.

We can see that angle DOC is central angle and $m\angle DOC=60^o$ and arc DC subtends to central angle, therefore, the measure of arc DC will be 60 degrees.

B. Since we are told that arcs AB and CD are congruent and measure of arc DC is 60 degrees, therefore, measure of arc AB will be 60 degrees as well.

C. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Measure of Arc AB is 60 degrees, so by inscribed angle theorem the measure of angle ACB will be half the measure of AB.

$m\angle ACB=\frac{1}{2}\times \text{The measure of arc AB}$

$m\angle ACB=\frac{1}{2}\times 60^o$

$m\angle ACB=30^o$

Therefore, measure of angle ACB will be 30 degrees.

D. We can see that angle DOC and AOD form a linear pair of angles, so they will add up-to 180 degrees.

$m\angle DOC+m\angle AOD=180^o$

Upon substituting measure of angle DOC we will get,

$60^o+m\angle AOD=180^o$

$60^o-60^o+m\angle AOD=180^o-60^o$

$m\angle AOD=120^o$

Therefore, measure of angle AOD will be 120 degrees.

E. Since we know that angle inscribed in a semicircle is always a right angle. We can see that angle ABC is angle inscribed in the semicircle as AC is the diameter of our given circle, therefore, measure of angle ABC will be 90 degrees.

F. Since we know that arc measure of a semicircle is 180 degrees. We can see that arc ABC is arc of the semicircle, so we can set an equation as:

$\text{Measure of arc AB+ Measure of Arc BC}=180^o$

Upon substituting measure of arc AB we will get,

$60^o+\text{Measure of Arc BC}=180^o$

$60^o-60^o+\text{Measure of Arc BC}=180^o-60^o$

$\text{Measure of Arc BC}=120^o$

Therefore, measure of arc BC is 120 degrees.

What is the measure of arc KL?

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