Mathematics: What is the formula to find the measure of each angle of a regular polygon

What is the formula to find the measure of each, №15224965, 30.05.2022 10:28

Mathematics

IF YOU GET THIS RIGHT I WILL MARK BRAIN.LY DO NOT ANSWER IF YOU DO NOT KNOW OR YOU WILL GET REPORTED This is geometry through and through. Plus a little trig thrown in for fun. If you inscribe an equilateral triangle inside a circle and the triangle has side lengths of 12, you have part of what you need to use Pythagorean s Theorem to find the hypotenuse of the triangle which is also the radius of the circle. First, use the formula 360/3 to find that the central angle measure of each angle INSIDE a triangle is 120. So you have 3 triangles within

Step-by-step answer

P Answered by PhD

1

Side of equilateral Triangle =12 inch

Let r be the radius of Smallest circle which fits inside the triangle.

Theorem Which will be Used

→The Point of intersection of end point of radius and tangent through that end point makes an angle of 90°.

→Angle Subtended by an arc at the center is twice the angle subtended at any point on the circle.

→Perpendicular from the center of the circle to the chord bisects the chord.

→ Area of Equilateral Triangle

→Area of Triangle

⇒ Radius of the smallest circle

→ Area of Equilateral Triangle having side 12 inches

(1)

→Area of 3 Triangle having base =12 inches and height =r inches

(2)

Equating (1) and (2), that is both the Areas are equal.

⇒Radius of the largest circle

Each Interior angle of equilateral Triangle=60°

∠AOC=2×60°=120°Angle Subtended by an arc at the center is twice the angle subtended at any point on the circle.

r=Radius of circle

→∠AOC+∠CAO+∠ACO=180°---Angle sum property of triangle.

→ 120°+2∠CAO=180°[OA=OC, →∠CAO=∠OCAAngle Opposite to equal side of a triangle are equal.]

→2∠CAO=180°-120°

→2∠CAO=60°

→∠CAO=30°Dividing both sides by, 2

→∠MAO+∠AMO+∠AOM=180°---Angle sum property of triangle.

→∠MAO+90°+60°=180°

→∠MAO=180°-150°

→∠MAO=30°

In ΔOMA

AC=12 inches

AM=MC=6 inches--Perpendicular from the center of the circle to the chord bisects the chord.

:

Mathematics

IF YOU GET THIS RIGHT I WILL MARK BRAIN.LY DO NOT ANSWER IF YOU DO NOT KNOW OR YOU WILL GET REPORTED This is geometry through and through. Plus a little trig thrown in for fun. If you inscribe an equilateral triangle inside a circle and the triangle has side lengths of 12, you have part of what you need to use Pythagorean s Theorem to find the hypotenuse of the triangle which is also the radius of the circle. First, use the formula 360/3 to find that the central angle measure of each angle INSIDE a triangle is 120. So you have 3 triangles within

Step-by-step answer

P Answered by PhD

1

Side of equilateral Triangle =12 inch

Let r be the radius of Smallest circle which fits inside the triangle.

Theorem Which will be Used

→The Point of intersection of end point of radius and tangent through that end point makes an angle of 90°.

→Angle Subtended by an arc at the center is twice the angle subtended at any point on the circle.

→Perpendicular from the center of the circle to the chord bisects the chord.

→ Area of Equilateral Triangle

→Area of Triangle

⇒ Radius of the smallest circle

→ Area of Equilateral Triangle having side 12 inches

(1)

→Area of 3 Triangle having base =12 inches and height =r inches

(2)

Equating (1) and (2), that is both the Areas are equal.

⇒Radius of the largest circle

Each Interior angle of equilateral Triangle=60°

∠AOC=2×60°=120°Angle Subtended by an arc at the center is twice the angle subtended at any point on the circle.

r=Radius of circle

→∠AOC+∠CAO+∠ACO=180°---Angle sum property of triangle.

→ 120°+2∠CAO=180°[OA=OC, →∠CAO=∠OCAAngle Opposite to equal side of a triangle are equal.]

→2∠CAO=180°-120°

→2∠CAO=60°

→∠CAO=30°Dividing both sides by, 2

→∠MAO+∠AMO+∠AOM=180°---Angle sum property of triangle.

→∠MAO+90°+60°=180°

→∠MAO=180°-150°

→∠MAO=30°

In ΔOMA

AC=12 inches

AM=MC=6 inches--Perpendicular from the center of the circle to the chord bisects the chord.

:

Mathematics

What is the formula to find the measure of each interior angle of a regular polygon

Step-by-step answer

P Answered by Specialist

14

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.

Step-by-step explanation:

There ya go.. :)

Mathematics

What is the formula to find the measure of each interior angle of a regular polygon

Step-by-step answer

P Answered by Master

14

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.

Step-by-step explanation:

There ya go.. :)

Mathematics

Will give brainliest if you ! 20 points! david and his dad were going camping. when they went into the garage to get their tent they noticed it was ripped. david’s dad said he could fix the tent. he would buy some new material to cover the one rectangular side that ripped. how much material does he need to cover the one rectangular side of the tent with the rip? justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. to figure out how much material david and his dad need to cover we must figure

Step-by-step answer

P Answered by PhD

3

Part 1) $54\ ft^{2}$

Part 2) The surface area is $SA=(7\frac{\sqrt{95}}{2}+171)\ ft^{2}$ or $SA=205.11\ ft^{2}$

Part 3) $V=63\frac{\sqrt{95}}{4}\ ft^{3}$ or $V=153.51\ ft^{3}$

Step-by-step explanation:

Part 1) How much material does he need to cover the one rectangular side of the tent with the rip?

we know that

The area of a rectangle is equal to

A=LW

we have

$L=9\ ft$

$W=6\ ft$

substitute the values

$A=(9)(6)=54\ ft^{2}$

Part 2) If David’s dad wanted to re-cover the whole tent including the bottom, how much material would he need?

we know that

The surface area of a triangular prism (the tent) is equal to

SA=2B+PL

where

B is the area of the triangular face

P is the perimeter of the triangular face

L is the length of the triangular prism

Find the area of the triangular face B

Note The height of the triangle cannot be equal to 6 ft. The height of a right triangle cannot be equal to the hypotenuse. The height must be calculated by applying Pythagoras theorem

$B=\frac{1}{2}bh$

we have

$b=7\ ft$

Find the height applying the Pythagoras Theorem

substitute the values

$h^{2}=6^{2}-(7/2)^{2}$

$h^{2}=95/4$

$h=\frac{\sqrt{95}}{2}\ ft$

substitute

$B=\frac{1}{2}(7)(\frac{\sqrt{95}}{2})$

$B=7\frac{\sqrt{95}}{4}\ ft^{2}$

Fin the perimeter of the triangular base P

$P=6+6+7=19\ ft$

Find the surface area SA

$SA=2(7\frac{\sqrt{95}}{4})+(19)(9)$

$SA=(7\frac{\sqrt{95}}{2}+171)\ ft^{2}$ -----> exact value

or

$SA=205.11\ ft^{2}$ -----> approximate value

Part 3) What is the volume of the tent?

we know that

The volume of the tent is equal to

V=BL

where

B is the area of the triangular face

L is the length of the tent

we have

$B=7\frac{\sqrt{95}}{4}\ ft^{2}$

$L=9\ ft$

substitute

$V=(7\frac{\sqrt{95}}{4})(9)$

$V=63\frac{\sqrt{95}}{4}\ ft^{3}$ -----> exact value

or

$V=153.51\ ft^{3}$ -----> approximate value

Mathematics

Will give brainliest if you ! 20 points! david and his dad were going camping. when they went into the garage to get their tent they noticed it was ripped. david’s dad said he could fix the tent. he would buy some new material to cover the one rectangular side that ripped. how much material does he need to cover the one rectangular side of the tent with the rip? justify your answer using equations/formulas, models, and/or words to explain your mathematical reasoning. to figure out how much material david and his dad need to cover we must figure

Step-by-step answer

P Answered by PhD

3

Part 1) $54\ ft^{2}$

Part 2) The surface area is $SA=(7\frac{\sqrt{95}}{2}+171)\ ft^{2}$ or $SA=205.11\ ft^{2}$

Part 3) $V=63\frac{\sqrt{95}}{4}\ ft^{3}$ or $V=153.51\ ft^{3}$

Step-by-step explanation:

Part 1) How much material does he need to cover the one rectangular side of the tent with the rip?

we know that

The area of a rectangle is equal to

A=LW

we have

$L=9\ ft$

$W=6\ ft$

substitute the values

$A=(9)(6)=54\ ft^{2}$

Part 2) If David’s dad wanted to re-cover the whole tent including the bottom, how much material would he need?

we know that

The surface area of a triangular prism (the tent) is equal to

SA=2B+PL

where

B is the area of the triangular face

P is the perimeter of the triangular face

L is the length of the triangular prism

Find the area of the triangular face B

Note The height of the triangle cannot be equal to 6 ft. The height of a right triangle cannot be equal to the hypotenuse. The height must be calculated by applying Pythagoras theorem

$B=\frac{1}{2}bh$

we have

$b=7\ ft$

Find the height applying the Pythagoras Theorem

substitute the values

$h^{2}=6^{2}-(7/2)^{2}$

$h^{2}=95/4$

$h=\frac{\sqrt{95}}{2}\ ft$

substitute

$B=\frac{1}{2}(7)(\frac{\sqrt{95}}{2})$

$B=7\frac{\sqrt{95}}{4}\ ft^{2}$

Fin the perimeter of the triangular base P

$P=6+6+7=19\ ft$

Find the surface area SA

$SA=2(7\frac{\sqrt{95}}{4})+(19)(9)$

$SA=(7\frac{\sqrt{95}}{2}+171)\ ft^{2}$ -----> exact value

or

$SA=205.11\ ft^{2}$ -----> approximate value

Part 3) What is the volume of the tent?

we know that

The volume of the tent is equal to

V=BL

where

B is the area of the triangular face

L is the length of the tent

we have

$B=7\frac{\sqrt{95}}{4}\ ft^{2}$

$L=9\ ft$

substitute

$V=(7\frac{\sqrt{95}}{4})(9)$

$V=63\frac{\sqrt{95}}{4}\ ft^{3}$ -----> exact value

or

$V=153.51\ ft^{3}$ -----> approximate value

Mathematics

If the two angles are complementary, find the measure of each of angle. I am having trouble decoding this problem in it it says 7f and 2f what is the formula for this problem

Step-by-step answer

P Answered by Specialist

1

f=10

Step-by-step explanation:

I don't know a formula for this but I can see that <CRE is a 90° angle so 7f+2f=90 and if f=10 7f=70 and 2f=20 which fits

Mathematics

If the two angles are complementary, find the measure of each of angle. I am having trouble decoding this problem in it it says 7f and 2f what is the formula for this problem

Step-by-step answer

P Answered by Specialist

1

f=10

Step-by-step explanation:

I don't know a formula for this but I can see that <CRE is a 90° angle so 7f+2f=90 and if f=10 7f=70 and 2f=20 which fits

Mathematics

logo Mathematics Mathematics, 13.11.2020 02:40, alexabessin Jennifer and her three cousins drove 165 miles to visit their grandmother. Their car got 24 miles per gallon during the trip. They drove at an average rate of 55 miles per hour and the gasoline for the trip cost $8.94. Calculate each of the following and explain in a complete sentence how you solved the problem. If your sentence has a rate, underline it. 1. Gallons of gasoline used 2. Hours of travel 3. Average feet per second 4. Dollars per hour 5. Dollars per passenger 6. Dollars per

Step-by-step answer

P Answered by Master

Answer:

See below

Step-by-step explanation:

Solution is given in the picture below. All the values are calculated.

Mathematics

What is the FORMULA of the measure of each Exterior Angle of a Regular Polygon.

Step-by-step answer

P Answered by Specialist

6

360/n=mE

Step-by-step explanation:

The formula to find the measure of an exterior angle you divide 360 by the amount of sides (n) and that is the measure of your exterior angles.

What is the formula to find the measure of each angle of a regular polygon

Step-by-step answer

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