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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 49 Page 528

∠ ZWX and ∠ ZYX are congruent. Use the Polygon Interior Angles Sum Theorem to write an equation.

m∠ ZYX = 100^(∘)

Practice makes perfect

We want to find the measure of ∠ ZYX in our kite. In a kite, exactly one pair of opposite angles are congruent. In our kite, these angles are ∠ ZWX and ∠ ZYX. Since m∠ ZWX= 10x it must also be that m∠ ZYX= 10x. Let's add these angle measures along with the rest of the angles that have been given.

Recall the Polygon Interior Angles Sum Theorem

Polygon Interior Angles Sum Theorem
The sum of the interior angle measures of an n-sided polygon is (n-2)180^(∘).

By substituting n= 4 into the formula, we can determine the sum of the kite's interior angles. ( 4-2)180^(∘)=360^(∘) When we know the sum of the kite's interior angles, we can set the sum of the angle's equal to this number. 4x+ 10x+ 10x+ 120^(∘)=360^(∘) Let's solve this equation to find x.

4x+10x+10x+120^(∘)=360^(∘)

▼

Solve for x

Add terms

24x+120^(∘)=360^(∘)

LHS-120^(∘)=RHS-120^(∘)

24x=240^(∘)

.LHS /24.=.RHS /24.

x=10^(∘)

Finally, we will substitute x= 10^(∘) into the expression for m∠ ZYX to find its measure. m∠ ZYX=10( 10^(∘))=100^(∘)

Subchapter links

Exercises p.526-530