Exercise 37 Page 599

We will find the measure of ∠ K.

If a quadrilateral is a kite, then exactly one pair of opposite angles are congruent. In this case, since ∠ J is not congruent to angle L, we have ∠ K ≅ ∠ M. Let's add this to the diagram.

Using the Polygon Interior Angles Sum Theorem, we know that the sum of the interior angles in JKLM is 360^(∘). 59^(∘)+m∠ K+67^(∘)+m∠ M=360^(∘) Let's solve for m∠ K by performing inverse operations.

∠ J +∠ K +∠ L +∠ M =360

SubstituteValues

Substitute values

59+∠ K+67+∠ M=360

Substitute

∠ M= ∠ K

59+∠ K+67+ ∠ K=360

AddTerms

Add terms

2∠ K+126=360

SubEqn

LHS-126=RHS-126

2∠ K=234

DivEqn

.LHS /2.=.RHS /2.

∠ K=117