Question

The exterior angles of a quadrilateral have measures of 72∘, 58∘, 2x∘, and 3x∘. How do I find the value of x?

Answer 1

`x = 46`

The sum of all exterior angles of any polygon is always `360` degrees.

Explanation:

In any given polygon, whether there are `3` sides or `16` sides, the sum of all exterior angles is always `360^@`.

Therefore, your equation would be

`72^@ + 58^@ + (2x)^@ + (3x)^@ = 360^@`

Simplify to get the answer.

`72 + 58 + 2x + 3x = 360`

`130 + 5x = 360`

`5x = 230`

`x = 46`