Exercise 27 Page 527

We will find the measure of ∠ Z.

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. In this case, we have ∠ X≅ ∠ Z. 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^(∘). 90^(∘)+m∠ X + 120^(∘)+m∠ Z=360^(∘) Let's solve for m∠ Z by performing inverse operations.