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McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 7 Page 526

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent.

70^(∘)

Practice makes perfect

We want to find the measure of ∠ C.

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. In this case, we have ∠ D≅ ∠ B. Let's add this to the diagram.

Using the Polygon Interior Angles Sum Theorem we know that the sum of the interior angles in ABCD is 360^(∘). 120^(∘)+85^(∘)+m∠ C+85^(∘)=360^(∘) Let's solve for m∠ C by performing inverse operations.

120^(∘)+85^(∘)+m∠ C+85^(∘)=360^(∘)

AddTerms

Add terms

290^(∘)+m ∠ C=360^(∘)

SubEqn

LHS-290^(∘)=RHS-290^(∘)

m ∠ C =70^(∘)