In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o, Calculate ∠XYZ

  • A 50o
  • B 62o
  • C 112o
  • D 115o
waec 1999mathematics

The correct answer is D. 115o

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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