1.

In figure, find ∠A.

Answer»

At point B,

100° + ∠ABC = 180° (linear pair angles)

∠ABC = 80°

At point C,

∠DCB + 95° = 180°

⇒ ∠DCB = 85°

Similarly at D,

82° + ∠CDA = 180° (linear pair axiom)

∠CDA = 180° – 82° = 98°

Now in quadrilateral ABCD

∠A + 80° + 85° + 98° = 360° (by angle sum property of a quadrilateral)

⇒ ∠A = 360° – 263°

⇒ ∠A = 97°.


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