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