In Fig. 6.34, find the measures of ∠PON and ∠NPO.

Formula Used/Theory:-

→ Angle sum property

Sum of all angles of triangle is 180°

→ Exterior angle is equal to sum of interior opposite angles

In Δ LOM

∠LOP = ∠MLO + ∠LMO

= 70° + 20° = 90°

In Δ PON

∠LOP = ∠NPO + ∠PNO

90° = ∠NPO + 70°

∠NPO = 90° - 70° = 20°

∠NPO + ∠PNO + ∠PON = 180° (Angle sum property)

20° + 70° + ∠PON = 180°

∠PON = 180° - 90°

∠PON = 90°

Result:- ∠PON = 90°; ∠NPO = 20°