Question

Given the following figure, what is the measure of angle B?

Answer 1

132°

Explanation:

Sum of the interior angles of a polygon is given by the formula:

`(n-2)*180`

Where
`n` is the number of sides of the polygon.

The figure shows a 5 sided polygon (aka Pentagon). So the sum of all the angles is:

Sum =
`(5-2)*180\\=3*180\\=540`

If we add up all the expressions/angles given and equate to 540, we can figure out
`x`. So:

`84+13x+6+9x-16+92+12x=540\\34x+166=540\\34x=540-166\\34x=374\\x=(374)/(34)=11`

But angle B measures
`12x`, so plugging in
`x=11`, we have:

Angle B =
`12x=12(11)=132`°

Second answer is right.