Exercise 52 Page 740

We want to find the measure of ∠ YWZ, given that m∠ XZY=56^(∘). A rhombus is symmetric about its diagonals. Therefore ∠ XZY and ∠ YWX are congruent, which means they have the same measure.

In a rhombus, the diagonals bisect opposite angles. In our case the diagonal WZ bisects the angles ∠ YWX and ∠ XZY.

The measure of m∠ YWZ must be half the measure of m∠ YWX. With this information, we can write and solve an equation that contains m∠ YWZ.

m∠ YWZ=1/2m∠ YWX

Substitute

m∠ YWX= 56^(∘)

m∠ YWZ=1/2( 56^(∘))

▼

Evaluate right-hand side

MoveRightFacToNumOne

1/b* a = a/b

m∠ YWZ=56^(∘)/2

CalcQuot

Calculate quotient

m∠ YWZ=28^(∘)