Question 166
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

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Solution

Let ABCD be a quadrilateral, such that
$∠ A = ∠ C, ∠ B = ∠ D$ and also $∠ A + ∠ C = 180^{\circ}, ∠ B + ∠ D = 180^{\circ}$
Now, $∠ A + ∠ A = 180^{\circ}$ [ $∵ ∠ C = ∠ A$ ]
$\Rightarrow 2 ∠ A = 180^{\circ} \Rightarrow ∠ A = 90^{\circ} S i m i l a r l y, ∠ B = 90^{\circ}$
Hence, each angle is a right angle.

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Question 166 Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.

Let ABCD be a quadrilateral, such that ∠A=∠C,∠B=∠D and also ∠A+∠C=180∘,∠B+∠D=180∘ Now, ∠A+∠A=180∘ [∵∠C=∠A] ⇒2∠A=180∘⇒∠A=90∘Similarly,∠B=90∘ Hence, each angle is a right angle.

Question 166
Both the pairs of opposite angles of a quadrilateral are equal and supplementary. Find the measure of each angle.