Question

In the following figure, find the measures of ∠PON and ∠NPO.

Answer 1

In ∆LOM,

∠LOM + ∠OLM + ∠OML = 180°  ...[Angle sum property]

⇒ ∠LOM + 70° + 20° = 180°

⇒ ∠LOM = 180° – 70° – 20° = 90°

∠LOM = ∠PON  ...[Vertically opposite angles]

∴ ∠PON = 90°

Now, in ΔΡΟΝ,

∠PON + ∠ONP + ∠NPO = 180° ...[Angle sum property]

⇒ 90° + 70° + ∠NPO = 180°

⇒ ∠NPO = 180° – 90° – 70° = 20°

Thus, ∠PON = 90° and ∠NPO = 20°