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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 6 Page 504

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

Let's find the value of each interior angle.

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 substitute 4 for n and solve our equation for x.

x+(2x-16)+2x+(x+10)=(n-2)* 180

▼

Solve for x

x+(2x-16)+2x+(x+10)=({\color{#0000FF}{4}}-2)\cdot 180

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Subtract term

x+(2x-16)+2x+(x+10)=2* 180

Multiply

x+(2x-16)+2x+(x+10)=360

Remove parentheses

x+2x-16+2x+x+10=720-360

Add and subtract terms

6x-6=360

LHS+6=RHS+6

6x=366

.LHS /6.=.RHS /6.

x=61

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

Measure of Interior Angle	x=61	Simplified
x	61	61
2x-16	2( 61)-16	106
2x	2( 61)	122
x+10	( 61)+10	71

Let's add these measures to our diagram.