Question

examine the relationships that exist in the diagram below. find the measures of angles a, b, c, and d. remember that you can find the angles in any order, depending on the angle relationships you use.

Answer 1

m∠a = 97°

m∠b = 15°

m∠c = 68°

m∠d = 68°

Explanation:

Since WY and RZ are parallel lines and XR is a transverse,

m∠XWY = m∠XRZ

a = 97°

m∠WYX = 180° - 112° = 68°

In ΔXYW,

m∠WXY = 180° - (m∠XWY + m∠WYX)

= 180° - (a + 68°)

= 180 - (97 + 68)

= 180 - 165

= 15°

b = 15°

Since WY and RZ are the parallel lines and XZ is a transverse,

m∠WYX = m∠RZX = 68°

c = 68°

m∠d = m∠c [Alternate interior angles]

d = 68°