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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 5 Page 504

Use the Polygon Angle-Sum Theorem. How many sides does the polygon have?

We have been asked to find the measure of each of the interior angles of the given quadrilateral.

We will start by finding the value of x. Recall the Polygon Angle-Sum Theorem.

Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of a regular n -gon is given by: (n-2)* 180^(∘)

In this case, expressions are given for the measures of the interior angles. We can write an equation where the sum of these expressions is equal to (n-2)* 180^(∘). x + (4x - 26) + x + (2x + 18) = (n - 2) * 180^(∘) Our polygon has 4 sides, so we can substitute 4 for n and solve our equation for x.

x+(4x-26)+x+(2x+18)=(n-2)* 180

n= 4

x+(4x-26)+x+(2x+18)=( 4-2)* 180

▼

Solve for x

Subtract term

x+(4x-26)+x+(2x+18)=2* 180

Multiply

x+(4x-26)+x+(2x+18)=360

Remove parentheses

x+4x-26+x+2x+18=360

Add and subtract terms

8x-8=360

LHS+8=RHS+8

8x=368

.LHS /8.=.RHS /8.

x=46

Now that we know the value of x, we can find the measures of the interior angles of the quadrilateral.

Measure of Interior Angle	x=46	Simplified
x	46	46
4x-26	4( 46)-26	158
2x+18	2( 46)+18	110

Let's add these measurements to our quadrilateral.