Question

how do i prove angle x and angle yzv are supplementary

Answer 1

Triangle XWV is an equilateral triangle(every angle is 60). So both angle V's are vertical angles, which means the are the same(60). Y is 90. So once you have 60 and 90 in triangle YZV, you know the last angle(Z) is 30. But since angle Z is 30 and angle X is 60, they are complementary and not supplementary(which adds up to 180)