Exercise 7 Page 526

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^(∘)