McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
Mid-Chapter Quiz
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Exercise 11 Page 504

71

Let's find the value of x for the given figure.

Recall the Polygon Exterior Angle-Sum Theorem.

Polygon Exterior Angle-Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360^(∘).

In this case, expressions are given for the measures of the exterior angles. We can write an equation where the sum of these expressions is equal to 360^(∘). (x - 10) + (x + 15) + 106 + (2x - 35) = 360 Let's solve for x.
(x-10)+(x+15)+106+(2x-35)=360
Solve for x
x-10+x+15+106+2x-35=360
4x+76=360
4x=284
x=71