Question

The sides of a five sided polygon are produced in order. If the measures of exterior angles so obtained are x° , (2x)°, (3x)°, (4x)°and (6x)°, find the value of x.

Answer 1

Answer

• The value of x = 22.5°.

Given

• A five sided polygon ( pentagon ) whose exterior angles measure x, 2x, 3x, 4x and 6x.

To Find

• The value of x.

Step By Step Explanation

We know that,

The sum of all the exterior angles = 360°

Equation :

So let's form an equation from the given information.

$\bigstar\underline{ \boxed{ \bold{ \red{x + 2x + 3x + 4x + 6x = 360}}}}$

Solution of the equation :

So let's solve the above equation to find the value of x.

$\longmapsto \sf x + 2x + 3x + 4x + 6x = 360 \\ \\ \longmapsto \sf 16x = 360 \\ \\ \longmapsto \sf x = \cancel\cfrac{360}{16} \\ \\ \dag \: \: \: {\boxed {\bold{ \green{x = 22.5}}}}$

Therefore, the value of x = 22.5°.

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