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.

∠ W +∠ X +∠ Y +∠ Z =360

SubstituteValues

Substitute values

90+∠ X+120+∠ Z=360

Substitute

∠ X= ∠ Z

90+ ∠ Z+120+∠ Z=360

AddTerms

Add terms

2∠ Z+210=360

SubEqn

LHS-210=RHS-210

2∠ Z=150

DivEqn

.LHS /2.=.RHS /2.

∠ Z=75