Mathematics: Which angle is a vertical to

Which angle is a vertical to, №9081529, 25.02.2021 02:15

Mathematics

1. part a which theorems or postulates allow you to find the value of y? a) vertical angles theorem and triangle angle-sum theorem b) triangle exterior angles theorem and vertical angles theorem c) triangles angle-sum theorem and angles addition postulate d) angles addition postulate and triangles exterior angles theorem part b find the value of each variable a) x=80, y=100 b) x=80, y=80 c) x=100, y=80 d) x=100, y=100 2. find m 1 a) 57 b) 63 c) 117 d) 123 3. which theorems or postulates could you use to find the measure of angle 1 in the previous

Step-by-step answer

P Answered by PhD

5

The correct answer for Number 1 is

A.

EXPLANATION

First we apply the vertical angles theorem to transfer x into the triangle. That is,

x=y

Next, we use the triangle angle sum theorem to write an equation in x, which is

x+70+30=180

We can solve this equation for x.

Part B

We now solve the equation to obtain,

x+100=180

This gives us,

x=80

and

The correct answer for this part is B.

2)

By the triangle exterior angle theorem,

The correct answer for this part is D.

3) The correct answer is the Triangle exterior angle theorem.

This theorem says that the sum of any two adjacent interior angles of a triangle equals the exterior angle opposite to them.

4) Using the triangle angle sum theorem, we can solve for x.

So we are adding all the angles in the triangle and equate them to 180.

(2x+4)+(2x-9)+x=180

We group like terms to obtain,

2x+2x+x=180+9-4

This simplifies to,

5x=185

we divide both sides by 5 to get,

$x=\frac{185}{5}=37$

The correct answer for this question 4 is C

Mathematics

1. part a which theorems or postulates allow you to find the value of y? a) vertical angles theorem and triangle angle-sum theorem b) triangle exterior angles theorem and vertical angles theorem c) triangles angle-sum theorem and angles addition postulate d) angles addition postulate and triangles exterior angles theorem part b find the value of each variable a) x=80, y=100 b) x=80, y=80 c) x=100, y=80 d) x=100, y=100 2. find m 1 a) 57 b) 63 c) 117 d) 123 3. which theorems or postulates could you use to find the measure of angle 1 in the previous

Step-by-step answer

P Answered by PhD

5

The correct answer for Number 1 is

A.

EXPLANATION

First we apply the vertical angles theorem to transfer x into the triangle. That is,

x=y

Next, we use the triangle angle sum theorem to write an equation in x, which is

x+70+30=180

We can solve this equation for x.

Part B

We now solve the equation to obtain,

x+100=180

This gives us,

x=80

and

The correct answer for this part is B.

2)

By the triangle exterior angle theorem,

The correct answer for this part is D.

3) The correct answer is the Triangle exterior angle theorem.

This theorem says that the sum of any two adjacent interior angles of a triangle equals the exterior angle opposite to them.

4) Using the triangle angle sum theorem, we can solve for x.

So we are adding all the angles in the triangle and equate them to 180.

(2x+4)+(2x-9)+x=180

We group like terms to obtain,

2x+2x+x=180+9-4

This simplifies to,

5x=185

we divide both sides by 5 to get,

$x=\frac{185}{5}=37$

The correct answer for this question 4 is C

Mathematics

Will get 1. part a which theorems or postulates allow you to find the value of y? a) vertical angles theorem and triangle angle-sum theorem b) triangle exterior angles theorem and vertical angles theorem c) triangles angle-sum theorem and angles addition postulate d) angles addition postulate and triangles exterior angles theorem part b find the value of each variable a) x=80, y=100 b) x=80, y=80 c) x=100, y=80 d) x=100, y=100 2. find m 1 a) 57 b) 63 c) 117 d) 123 3. which theorems or postulates could you use to find the measure of angle 1 in the

Step-by-step answer

P Answered by PhD

14

Answers:

1.

Part A. Option a) vertical angles theorem and triangle angle-sum theorem

Part B. Option b) x=80, y=80

2. Option d) 123

3. Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Option c) x=37

Solution:

1. Part A

First, you can find x using the triangle angle-sum theorem: The sum of the interior angles of any triangle must be equal to 180°.

Second, you can apply the vertical angles theorem to find y: the angles opposite by the vertex must be congruent.

Then, the answer is option a) vertical angles theorem and triangle angle-sum theorem.

1. Part B.

First: Triangle angle-sum theorem

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are x°, 30°, and 70°, then:

x°+30°+70°=180°

(x+30+70)°=180°

(x+100)°=180°

x+100=180

Solving for x: Subtracting 100 both sides of the equation:

x+100-100=180-100

x=80

Second: Vertical angles theorem: The angles opposite by the vertex must be congruent:

In the figure, the angles x° and y° are opposite by the vertex, then they must be congruent:

y°=x°

y=x

and x=80, then:

y=80

Option b) x=80, y=80

2. The <1 is an exterior angle of the triangle in the figure, and according with the Triangle Exterior Angle Theorem, an exterior angle of a triangle must be equal to the sum of the interior angles no adjacents to it:

<1=60°+63°

<1=123°

Option d) 123

3.

You can apply the Triangle Angle-Sum Theorem, to find the third interior angle of the triangle. With this angle you can find the exterior <1.

You can apply the Triangle Exterior Angle Theorem to find the exterior <1.

Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Using the Triangle angle-sum theorem:

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are (2x-9)°, x°, and (2x+4)°, then:

(2x-9)°+x°+(2x+4)°=180°

(2x-9+x+2x+4)°=180°

Adding similar terms:

(5x-5)°=180°

5x-5=180

Solving for x: Adding 5 both sides of the equation:

5x-5+5=180+5

Adding:

5x=185

Dividing both sides of the equation by 5:

(5x)/5=185/5

x=37

Option c) x=37

Mathematics

Will get 1. part a which theorems or postulates allow you to find the value of y? a) vertical angles theorem and triangle angle-sum theorem b) triangle exterior angles theorem and vertical angles theorem c) triangles angle-sum theorem and angles addition postulate d) angles addition postulate and triangles exterior angles theorem part b find the value of each variable a) x=80, y=100 b) x=80, y=80 c) x=100, y=80 d) x=100, y=100 2. find m 1 a) 57 b) 63 c) 117 d) 123 3. which theorems or postulates could you use to find the measure of angle 1 in the

Step-by-step answer

P Answered by PhD

14

Answers:

1.

Part A. Option a) vertical angles theorem and triangle angle-sum theorem

Part B. Option b) x=80, y=80

2. Option d) 123

3. Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Option c) x=37

Solution:

1. Part A

First, you can find x using the triangle angle-sum theorem: The sum of the interior angles of any triangle must be equal to 180°.

Second, you can apply the vertical angles theorem to find y: the angles opposite by the vertex must be congruent.

Then, the answer is option a) vertical angles theorem and triangle angle-sum theorem.

1. Part B.

First: Triangle angle-sum theorem

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are x°, 30°, and 70°, then:

x°+30°+70°=180°

(x+30+70)°=180°

(x+100)°=180°

x+100=180

Solving for x: Subtracting 100 both sides of the equation:

x+100-100=180-100

x=80

Second: Vertical angles theorem: The angles opposite by the vertex must be congruent:

In the figure, the angles x° and y° are opposite by the vertex, then they must be congruent:

y°=x°

y=x

and x=80, then:

y=80

Option b) x=80, y=80

2. The <1 is an exterior angle of the triangle in the figure, and according with the Triangle Exterior Angle Theorem, an exterior angle of a triangle must be equal to the sum of the interior angles no adjacents to it:

<1=60°+63°

<1=123°

Option d) 123

3.

You can apply the Triangle Angle-Sum Theorem, to find the third interior angle of the triangle. With this angle you can find the exterior <1.

You can apply the Triangle Exterior Angle Theorem to find the exterior <1.

Options 3 and 4:

Triangle Angle-Sum Theorem

Triangle Exterior Angle Theorem

4. Using the Triangle angle-sum theorem:

The sum of the interior angles of any triangle must be equal to 180°. The interior angles of the triangle in the figure are (2x-9)°, x°, and (2x+4)°, then:

(2x-9)°+x°+(2x+4)°=180°

(2x-9+x+2x+4)°=180°

Adding similar terms:

(5x-5)°=180°

5x-5=180

Solving for x: Adding 5 both sides of the equation:

5x-5+5=180+5

Adding:

5x=185

Dividing both sides of the equation by 5:

(5x)/5=185/5

x=37

Option c) x=37

Mathematics

Use the table to identify the relationship of the second sentence to the first sentence.1. if two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.. 2. if two angles are not vertical, then they are not nonadjacent angles formed by two intersecting lines. is it contrpositive or inverse or converse or biconditonal or logical equivalent. co = contrapositive bi = biconditional le = logical equivalent cv = converse in = inverse 1. if the measure of an angle is 90 degrees, then it is a right angle. 2.the measure

Step-by-step answer

P Answered by PhD

2

If the first statement is "if p then q", then
CO : if not q then not p (contrapositive)
BI : if p then q AND if q then p (bi conditional, p <-> q)
LE : either if p then q OR if not q then not p (logical equivalent)
IN : if not p then not q (inverse)
CV: if q then p (converse)

If two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.. . 2.

if p then q,
where
p: two angles are vertical
q: they are nonadjacent angles formed by two intersecting lines

If two angles are not vertical, then they are not nonadjacent angles formed by two intersecting lines.
means
if not p then not q

therefore the second statement is the inverse of the first.

Mathematics

Use the table to identify the relationship of the second sentence to the first sentence.1. if two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.. 2. if two angles are not vertical, then they are not nonadjacent angles formed by two intersecting lines. is it contrpositive or inverse or converse or biconditonal or logical equivalent. co = contrapositive bi = biconditional le = logical equivalent cv = converse in = inverse 1. if the measure of an angle is 90 degrees, then it is a right angle. 2.the measure

Step-by-step answer

P Answered by PhD

2

If the first statement is "if p then q", then
CO : if not q then not p (contrapositive)
BI : if p then q AND if q then p (bi conditional, p <-> q)
LE : either if p then q OR if not q then not p (logical equivalent)
IN : if not p then not q (inverse)
CV: if q then p (converse)

If two angles are vertical, then they are nonadjacent angles formed by two intersecting lines.. . 2.

if p then q,
where
p: two angles are vertical
q: they are nonadjacent angles formed by two intersecting lines

If two angles are not vertical, then they are not nonadjacent angles formed by two intersecting lines.
means
if not p then not q

therefore the second statement is the inverse of the first.

Mathematics

URGENT AT LEAST TAKE A LOOK 13. Assume that you have a square. What can you conclude from applying the law of detachment to this conditional? If you have a square, then you have a rectangle. A) You have a quadrilateral. B) All sides are the same length. C) Squares and rectangles are the same. D) You have a rectangle. 14. Which two theorems would justify that m∠4 = m∠6, given that m∠5 = m∠6 in the diagram below? IMAGE BELOW A) vertical angles theorem, consecutive interior angles theorem B) vertical angles theorem, alternate interior angles theorem

Step-by-step answer

P Answered by Master

6

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Mathematics

URGENT AT LEAST TAKE A LOOK 13. Assume that you have a square. What can you conclude from applying the law of detachment to this conditional? If you have a square, then you have a rectangle. A) You have a quadrilateral. B) All sides are the same length. C) Squares and rectangles are the same. D) You have a rectangle. 14. Which two theorems would justify that m∠4 = m∠6, given that m∠5 = m∠6 in the diagram below? IMAGE BELOW A) vertical angles theorem, consecutive interior angles theorem B) vertical angles theorem, alternate interior angles theorem

Step-by-step answer

P Answered by Master

6

d: please note I am not sure about this but look at my reasoning and maybe you can find your own answer that you are sure about.

D: i am sure about this.

Step-by-step explanation:

From what I looked up, i believe what you are talking about is deductive reasoning, which is based off of facts. It can't be a or b because that wasn't defined in the statement. Squares and rectangles are not the same thing since you can have a square that is a rectangle, but a rectangle that is not a square, so D is correct.

corresponding angles i believe since they are matching

I know that the 2 lines are parallel because 5 and 6 are alternate interior angles since they are on opposite sides.

4 and 6 are not vertical or right angles, so it must be d, also they follow what a corresponding angle is, which is them being matching.

Mathematics

Part a 3. which theorems or postulates allow you to find the value of y? [] vertical angles theorem and triangle angle-sum theorem [] triangle exterior angles theorem and vertical angles theorem [] triangle angle-sum theorem and angle addition postulate [] angle addition postulate and triangle exterior angles theorem part b 3. find the value of each variable. [] x = 80, y = 100 [] x = 80, y = 80 [] x = 100, y = 80 [] x = 100, y = 100

Step-by-step answer

P Answered by PhD

11

Definition: Vertical angles are the angles that are vertically opposite to each other when two lines intersect.

Vertical Angles Theorem: Vertical angles are congruent to each other.

Triangle Angle-Sum Theorem: The sum of the measures of the interior angles of a triangle is 180°.

The diagram shows triangle with to given angles. By the Triangle Angle-Sum Theorem you can find the measure of third angle. Angles x and y are vertical, then they are congruent.

Answer Part A: option A

By the Triangle Angle-Sum Theorem, x°+30°+70°=180°,

x°=80°

and

x°=y°=80°.

Answer part B: option B

Mathematics

Part a 3. which theorems or postulates allow you to find the value of y? [] vertical angles theorem and triangle angle-sum theorem [] triangle exterior angles theorem and vertical angles theorem [] triangle angle-sum theorem and angle addition postulate [] angle addition postulate and triangle exterior angles theorem part b 3. find the value of each variable. [] x = 80, y = 100 [] x = 80, y = 80 [] x = 100, y = 80 [] x = 100, y = 100

Step-by-step answer

P Answered by PhD

11

Definition: Vertical angles are the angles that are vertically opposite to each other when two lines intersect.

Vertical Angles Theorem: Vertical angles are congruent to each other.

Triangle Angle-Sum Theorem: The sum of the measures of the interior angles of a triangle is 180°.

The diagram shows triangle with to given angles. By the Triangle Angle-Sum Theorem you can find the measure of third angle. Angles x and y are vertical, then they are congruent.

Answer Part A: option A

By the Triangle Angle-Sum Theorem, x°+30°+70°=180°,

x°=80°

and

x°=y°=80°.

Answer part B: option B

Which angle is a vertical to

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