In the adjoining figure, ABCD is a parallelogram in which ∠A = 72°.

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 ​= ∠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

 

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