In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ
Attached Figure / Diagram
A
50o
B
62o
C
112o
D
115o
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
In triangle RXY, < RXY = < RYX (base angles of an isosceles triangle)
\(\implies\) 180^\circ - 62^\circ = 2 < RYX
118^\circ = 2 < RYX \(\implies\) < RYX = 59^\circ
In triangle RYZ, < RZY = 62^\circ (base angles of an isosceles triangle)
\(\therefore\) < RYZ = 180^\circ - (62^\circ + 62^\circ)
= 180^\circ - 124^\circ = 56^\circ
\(\therefore\) < XYZ = 56^\circ + 59^\circ
= 115^\circ
Source: WAEC / JAMB / NECO Classroom Archive (Record #26389)