Question

Find the measure of one exterior angle in each regular polygons

Answer 1

Answer:

Part 3) 51.4 degrees

Part 4) 36 degrees

Part 5) 165.6 degrees

Part 6) 128.6 degrees

Part 7) 90 degrees

Part 8) 147.3 degrees

Step-by-step explanation:

Part 3) Find the measure of one exterior angle in each regular polygon

we know that

In a regular polygon (polygon that have equal sides and equal angles) the measure of one exterior angle is equal to divide 360 degrees by the number of sides of the polygon

we have

A heptagon

The number of sides of the heptagon is 7 sides

so

$\frac{360}{7}= 51.4^o$

Part 4) Find the measure of one exterior angle in each regular polygon

we know that

In a regular polygon (polygon that have equal sides and equal angles) the measure of one exterior angle is equal to divide 360 degrees by the number of sides of the polygon

we have

A decagon

The number of sides of the decagon is 10 sides

so

$\frac{360}{10}= 36^o$

Part 5) Find the measure of one interior angle in each regular polygon

we know that

The measure of the interior angle in a regular polygon is given by the formula

$\frac{180^o(n-2)}{n}$

where

n is the number of sides

In this problem

we have

Regular 25-gon

so

n=25 sides

substitute in the formula

$\frac{180^o(25-2)}{25}=165.6^o$

Part 6) Find the measure of one interior angle in each regular polygon

we know that

The measure of the interior angle in a regular polygon is given by the formula

$\frac{180^o(n-2)}{n}$

where

n is the number of sides

In this problem

we have

Regular heptagon

so

n=7 sides

substitute in the formula

$\frac{180^o(7-2)}{7}=128.6^o$

Part 7) Find the measure of one interior angle in each regular polygon

we know that

The measure of the interior angle in a regular polygon is given by the formula

$\frac{180^o(n-2)}{n}$

where

n is the number of sides

In this problem

we have

square

so

n=4 sides

substitute in the formula

$\frac{180^o(4-2)}{4}=90^o$

Part 8) Find the measure of one interior angle in each regular polygon

we know that

The measure of the interior angle in a regular polygon is given by the formula

$\frac{180^o(n-2)}{n}$

where

n is the number of sides

In this problem

we have

11-gon

so

n=11 sides

substitute in the formula

$\frac{180^o(11-2)}{11}=147.3^o$