In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ
-
A.
50o -
B.
62o -
C.
112o -
D.
115o
Correct Answer: Option D
Explanation
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°