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प्रश्न
In the given figure, find the measures of ∠PON and ∠NPO.
उत्तर
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°
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