In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ
A.
50o
B.
62o
C.
112o
D.
115o
Correct answer is D
In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)
\(\implies\) 180° - 62° = 2 < RYX
118° = 2 < RYX \(\implies\) < RYX = 59°
In triangle RYZ, < RZY = 62° (base angles of an isosceles triangle)
\(\therefore\) < RYZ = 180° - (62° + 62°)
= 180° - 124° = 56°
\(\therefore\) < XYZ = 56° + 59°
= 115°