Question

The interior angles of a pentagon are x,x,2x, and 2x. What is the measure of the larger angles

Answer 1

The measure of larger angle is 180°

Explanation:

Given as :

For the pentagon

The measure of interior angles are

∠A = x ,

∠B = x ,

∠C = 2 x ,

∠D = 2 x ,

∠E = 3 x

We know, The sum of measure of all interior angles of pentagon = 540°

So, x + x + 2 x + 2 x + 3 x = 540°

or, 9 x = 540°

∴ x =
`(540)/(9)`

I.e x = 60°

So, The measure of angles are

∠A = 60° ,

∠B = 60° ,

∠C = 2 × 60° = 120° ,

∠D = 2 × 60° = 120°,

∠E = 3 × 60° = 180°

So, the measure of larger angle is 180°

Hence The measure of larger angle is 180° Answer