Question

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

Answer 1

Answer:

4x +2x=180

6x=180

x=30

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Answer 2

Given:

$\\\\\odot\:\:\tt Exterior\: Angle \:of \:a \:regular\: polygon \:= \:2x$

$\odot\:\: \tt Interior\: Angle \:of \:a \:regular\: polygon\: =\: 4x$

To Find:

Value of x

Answer:

Explanation:

We know that,

Sum of exterior angle and interior angle = 180°

So,

4x+2x=180°

6x=180°

$x=\dfrac{180^{\circ}}{6}$

x=30°

Therefore, the answer is 30°

Interior Angle = 4x => 4*30° => 120°

Exterior Angle = 2x => 2*30° => 60°

Other Formulas:

1) Sum of Interior Angles of a polygon where n is the number of sides of polygon= (2n - 4) * 90°

2)Number of sides of a polygon when exterior angle is given =$\frac{360^{\circ}}{x}$

where x is the exterior angle

3) Sum of all exterior angles of any polgon = 360°

4) Number of diagonals of n sided polygon = $\frac{n(n-1)}{2}-n$

5) Sum of exterior and interior angle of a polygon of n sides = 180°