Home » In the diagram above, |XR| = |RY| = |YZ| and ∠XRY = ∠YRZ = 62o,…

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

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°

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