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Question
In a parallelogram ABCD ∠C = 98°. Find ∠A and ∠B.
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Solution
ABCD is a parallelogram
∠C = 98°
∴ ∠A = ∠C = 98° ....(opposite angles of a parallelogram are equal)
∠A + ∠B +∠C + ∠D = 360° ....(Sum of all angles of a quadrilateral = 360°)
98° + ∠B + 98° + ∠D = 360°
∠B + 196 + ∠D = 360°
∠B + ∠D = 360° - 196°
∠B +∠D = 164°
But ∠B = ∠D ....(opposite angles of a parallelogram are equal)
⇒ 2∠B = 164°
⇒ ∠B = 82° = ∠D
Therefore,
∠B = 82°, ∠A = 98°.
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