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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Angles of Polygons

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Exercise 8 Page 480

Use the Polygon Exterior Angles Sum Theorem.

52^(∘)

Practice makes perfect

Let's find the value of x^(∘).

Recall the Polygon Exterior Angles Sum Theorem.

Polygon Exterior Angles 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. Using the theorem, we can write an equation where the sum of these expressions is equal to 360. (x+2)^(∘)+52^(∘)+2x^(∘)+88^(∘)+(x+10)^(∘) = 360^(∘) Let's solve it to find x.

(x+2)^(∘)+52^(∘)+2x^(∘)+88^(∘)+(x+10)^(∘)=360^(∘)

▼

Solve for x

Remove parentheses

x^(∘)+2^(∘)+52^(∘)+2x^(∘)+88^(∘)+x^(∘)+10^(∘)=360^(∘)

Add terms

4x^(∘)+152^(∘)=360^(∘)

LHS-152^(∘)=RHS-152^(∘)

4x^(∘)=208^(∘)

.LHS /4.=.RHS /4.

x^(∘)=52^(∘)

Subchapter links

Exercises p.479-483