Question

In the adjoining figure, ABCD is a parallelogram in which $\angle A={72}^{\circ }$. Calculate $\angle B,\angle Cand\angle D$.

Answer 1

ANSWER:
ABCD is parallelogram and ∠ A = 72° .
We know that opposite angles of a parallelogram are equal.
∴∠ A = ∠ C and ∠ B = ∠ D
∴ ∠C = ${72}^{\circ }$
∠ A and ∠B are adajcent angles.
i.e., ∠ A + ∠B = ${180}^{\circ }$
⇒ ∠B = ${180}^{\circ }$ − ∠ A
⇒ ∠B = ${180}^{\circ }$ − ${72}^{\circ }$ = ${108}^{\circ }$
∴ ∠B = ∠ D = ${108}^{\circ }$
Hence, ∠B = ∠ D = ${108}^{\circ }$ and ∠C = ${72}^{\circ }$