Mathematics, 30.03.2020 01:36 mihirkantighosh

Find the measure of one exterior angle in each regular polygons

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Answer from: 166386

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

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

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

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

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

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

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

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

n=11 sides

substitute in the formula

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

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Find the measure of one exterior angle in each regular polygons
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