To determine ∠ XYZ we should first find the measures of the congruent angles, ∠ XYW and ∠ WYZ, which are the result of bisecting ∠ XYZ.
From the previous exercise we know that x=8. By substituting this value into the expression for ∠ XYW and ∠ WYZ, we can find their measures.
Angle
Expression
x= 8
Simplify
∠ XYW
(3x-7)^(∘)
(3( 8)-7)^(∘)
17^(∘)
∠ WYZ
(2x+1)^(∘)
(2( 8)+1)^(∘)
17^(∘)
Since the two smaller congruent angles are both 17^(∘), the larger angle, ∠ XYZ, has to be double this size: 34^(∘).
