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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 53 Page 503

Recall the Polygon Exterior Angles Sum Theorem.

x=35

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. (3x+3)+(4x+4)+(x+1)+(2x+2)= 360 Let's solve the above equation to find x.

(3x+3)+(4x+4)+(x+1)+(2x+2)=360

▼

Solve for x

Remove parentheses

3x+3+4x+4+x+1+2x+2=360

Add terms

10x+10=360

LHS-10=RHS-10

10x=350

.LHS /10.=.RHS /10.

x=35

Extra

Measure of the Angles

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=35	Simplified
3x+3	3( 35)+3	108
4x+4	4( 35)+4	144
x+1	35+1	36
2x+2	2( 35)+2	72

Let's complete our diagram with the obtained information.

Subchapter links

Exercises p.499-503