In the diagram below, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62°,
MATHEMATICS
WAEC 1999
In the diagram below, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62°, Calculate ∠XYZ
- A. 50°
- B. 62°
- C. 112°
- D. 115°
Correct Answer: D. 115°
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°
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