Question

The measure of an exterior angle of a regular polygon is 2x and the measure of an interior angle is 4x. Use this relationship between interior and exterior angles to find the measure of one interior angle and exterior angle.

Answer 1

Step-by-step explanation:

2x + 4x = 180 (linear pair )

6x =180

x = 180÷6

x =30

30×2=60

30×4=120

Answer 2

The measure of exterior angle would be $2x=2\times 30=60^\circ$

The measure of interior angle would be $3x=3\times 30=90^\circ$

Step-by-step explanation:

Since we have given that

Measure of an exterior angle = 2x

Measure of an interior angle = 4x

So, using the relationship between interior and exterior angle would be

$2x+4x=180^\circ\\\\6x=180^\circ\\\\x=\dfrac{180}{6}\\\\x=30^\circ$

So, the measure of exterior angle would be $2x=2\times 30=60^\circ$

The measure of interior angle would be $3x=3\times 30=90^\circ$

# learn more:

The ratio between exterior angle and interior angle of a regular polygon is 1 :5 find the measure of each interior angle, find the measure of each exterior angle and the no. of sides of the polygon.

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