In the given figure, ABCD is a parallelogram in which ∠BAD = 75° and ∠CBD = 60°. Then, ∠BDC = ?
(a) 60°
(b) 75°
(c) 45°
(d) 50°

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Solution

(c) 45°

Explanation:
∠B = 180^o − ∠A
⇒ ∠B = 180^o − 75^o = 105^o
Now, ∠B = ∠ABD + ∠CBD
⇒ 105^o = ∠ABD + 60^o
⇒ ∠ABD = 105^o − 60^o = 45^o
⇒ ∠ABD = ∠BDC = 45^o (Alternate angles)

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In the adjoining figure, ABCD is a parallelogram in which $∠ B A D = 75^{\circ} a n d ∠ C B D = 60^{\circ}$ . Then, $∠ B D C =$ ?

(a) $60^{\circ}$

(b) $75^{\circ}$

(d) $50^{\circ}$

In the given figure, ABCD is a parallelogram. If AM bisects $∠ A$ and DM bisects $∠ D$ , then $∠ A M D$ = ____.

∠ D A B

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∠

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∠ A = 75^{\circ}

∠ B

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