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McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 71 Page 530

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

76

Practice makes perfect

We want to find the m∠ C in the given kite.

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^(∘). 74^(∘)+105^(∘)+x^(∘)+105^(∘)=360^(∘) Let's solve for x by performing inverse operations.

74^(∘)+105^(∘)+x^(∘)+105^(∘)=360^(∘)

AddTerms

Add terms

x^(∘)+284^(∘)=360^(∘)

SubEqn

LHS-284^(∘)=RHS-284^(∘)

x^(∘) =76^(∘)