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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
3. Tests for Parallelograms
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Exercise 54 Page 503

Recall the Polygon Exterior Angles Sum Theorem.

x=58

Practice makes perfect

We were asked to find the value of x in the given polygon.

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.

We can write an equation where the sum of the expressions is equal to 360. 2x+(x-10)+(x-14)+18+39+25+(x+12)= 360 Let's solve the above equation to find x.

2x+(x-10)+(x-14)+18+39+25+(x+12)=360
â–¼
Solve for x
RemovePar

Remove parentheses

2x+x-10+x-14+18+39+25+x+12=360
AddTerms

Add terms

5x+70=360
SubEqn

LHS-70=RHS-70

5x=290
DivEqn

.LHS /5.=.RHS /5.

x=58

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

Measure of exterior angle x=58 Simplified
x-10 58-10 48
x-14 58-14 44
x+12 58+12 70
2x 2( 58) 116

Let's complete our diagram with the obtained information.

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