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Question
Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
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Solution
Let ABCD be a quadrilateral,
Where ∠A = ∠C = 75° and ∠B = ∠D = x ...[say]
Then, by the angle sum property of a quadrilateral, we have
∠A + ∠B + ∠C + ∠D = 360°
⇒ 75° + x + 75° + x = 360°
⇒ 2x = 360° – 150°
⇒ 2x = 210°
⇒ x = 105°
Thus, other two angles are 105° each.
Since, opposite angles are equal, therefore the quadrilateral is a parallelogram.
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