Question

Using polygon STUVW what is m angle U ?

Answer 1

The m∠ U is 72°.

Explanation:

Given:

`\angle S = 90\\\angle T = 2x\\\angle U = x\\\angle V = 2x\\\angle W = 90\\`

To find :

`\angle U = x = ?`

Solution:

The sum of the measures of the interior angles of a polygon with 'n' sides is given as

`\textrm{sum of the measures of angle of a polygon with 'n' sides} = (n - 1)* 180`

Here we have n = 5 on substituting the values we get

`\angle S +\angle T + \angle U +\angle V + \angle W = (5 -2)* 180\\90 + 2x + x + 2x + 90 = 3* 180\\5x + 180 = 540\\5x = 540-180\\5x = 360\\x = (360)/(5)\\x = 72`

Therefore,

m∠ U is 72°.