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Question
In ∆XYZ, m∠Y = 90°. What kind of a pair do ∠X and ∠Z make?
Solution
In ∆XYZ,
∠X + ∠Y + ∠Z = 180° ...(Angle Sum property of triangle)
⇒ ∠X + 90° + ∠Z = 180°
∴ m∠X + 90° + m∠Z – 90° = 180° – 90° ...(Subtracting 90 from both sides)
⇒ ∠X + ∠Z = 90°
Since, the sum of the measures of the two angles is 90°.
Hence, ∠X and ∠Z are complementary angles.
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