Question

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

Answer 1

Answer:

132°

Step-by-step 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:

$84+13x+6+9x-16+92+12x=540\\34x+166=540\\34x=540-166\\34x=374\\x=\frac{374}{34}=11$

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

Angle B = $12x=12(11)=132$°

Second answer is right.