Question

In ∆XYZ, m∠Y = 90^°. What kind of a pair do ∠X and ∠Z make?

Answer 1

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.