a If ∠ XYZ is a straight angle, the sum of the three angles along XZ must sum to 180^(∘). Examining the diagram, the first thing we see is that ∠ WYV and ∠ VYZ are marked as identical. Let's add this information to the diagram.
Also, since ∠ WYX is marked as a right angle, we can calculate the sum of the three angles along ∠ XYZ.
With this, we know that m∠ XYZ cannot be a straight angle.
b From Part A, we know that the sum of the three angles along ∠ XYZ equals 182^(∘). To make it a straight angle, we have to reduce the sum of the angles by 2^(∘). Given that ∠ WYV≅ ∠ VYZ must hold true, we can either reduce the right angle by 2^(∘) or the congruent angles by 1^(∘) each.
