Question

In a right angled triangle MNO, ∠N = 90°, MO is extended to P. If ∠NOP = 128°, find the other two angles of ∆MNO

Answer 1

Given ∠N = 90°

MO is extended to P, the exterior angle ∠NOP = 128°

Exterior angle is equal to the sum of interior opposite angles.

∴ ∠M + ∠N = 128°

∠M + 90° = 128°

∠M = 128° – 90°

∠M = 38°

By angle sum property of triangle,

∴ ∠M + ∠N + ∠O = 180°

38° + 90° + ∠O = 180°

∠O = 180° – 128°

∠O = 52°

∴ ∠M = 38° and ∠O = 52°