Question:
In the adjoining figure, ABCD is a parallelogram in which ∠A = 72°. Calculate ∠B, ∠C and ∠D.
Solution:
ABCD is parallelogram and ∠A = 72°.
We know that opposite angles of a parallelogram are equal.
∴∠A = ∠C and ∠B = ∠D
∴ ∠C = 72o
∠A and ∠B are adajcent angles.
i.e., ∠A + ∠B = 180o
⇒ ∠B = 180o − ∠A
⇒ ∠B = 180o − 72o = 108o
∴ ∠B = ∠D = 108o
Hence, ∠B = ∠D = 108o and ∠C = 72o