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GenaCL600 [577]
3 years ago
7

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

Mathematics
1 answer:
scZoUnD [109]3 years ago
7 0

Answer:

132°

Step-by-step explanation:


<u>Sum of the interior angles of a polygon</u> is given by the formula:

(n-2)*180

Where n is the number of sides of the polygon.


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

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


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

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

<em>But angle B measures 12x, so plugging in x=11, we have:</em>

Angle B = 12x=12(11)=132°

Second answer is right.

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