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-BARSIC- [3]
3 years ago
9

The measure of an exterior angle of a regular polygon is 2x and the measure of an interior angle is 4x Find the measure of one i

nterior and exterior angle
Mathematics
1 answer:
kolbaska11 [484]3 years ago
6 0

Answer:

Part a) The measure of an exterior angle is 60°

Part b) The measure of an interior angle is 120°

Step-by-step explanation:

step 1

Find the value of x

we know that

A regular polygon has equal sides and equal interior angles

The sum of an interior angle plus an exterior angle must be equal to 180 degrees (supplementary angles)

so

2x+4x=180

solve for x

6x=180

x=30

step 2

Find the measure of an exterior angle

2x

substitute the value of x

2x=2(30)=60\°

step 3

Find the measure of an interior angle

4x

substitute the value of x

4x=4(30)=120\°

In this problem the regular polygon is a hexagon

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Since a regular polygon has equal interior angles, then the measure of the angle marked x is: 132°.

<h3>What is a Regular Polygon?</h3>

A regular polygon is any n-sided polygon that has equal interior angles and equal sides.

Thus:

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brainly.com/question/1592456

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The Larger of two numbers is 27 more than the smaller. When added together , the sum of the larger number and five times the sma
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