Exercise 26 Page 527

We will find the measure of ∠ X.

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 WXYZ is 360^(∘). 70^(∘)+m∠ X+56^(∘)+m∠ Z=360^(∘) Let's solve for m∠ X by performing inverse operations.

∠ W +∠ X +∠ Y +∠ Z =360

SubstituteValues

Substitute values

70+∠ X+56+∠ Z=360

Substitute

∠ Z= ∠ X

70+∠ X+56+ ∠ X=360

AddTerms

Add terms

2∠ X+126=360

SubEqn

LHS-126=RHS-126

2∠ X=234

DivEqn

.LHS /2.=.RHS /2.

∠ X=117