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McGraw Hill Integrated II, 2012

MH

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

▼

Solve for x

Remove parentheses

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

Add terms

5x+70=360

LHS-70=RHS-70

5x=290

.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.

Subchapter links

Exercises p.499-503