Question

ABCD is a parallelogram in which $\angle A={70}^{\circ }$. Compute $\angle B,\angle C,and\angle D.$

Answer 1

In ||gm ABCD,

$\angle A={70}^{\circ }$

But $\angle A+\angle B={180}^{\circ }$ (Sum of consecutive angles)

$\Rightarrow {70}^{\circ }+\angle B={180}^{\circ }$

$\Rightarrow \angle B={180}^{\circ }-{70}^{\circ }={110}^{\circ }$

But $\angle C=\angle Aand\angle D=\angle B$ (Opposite angles of a ||gm)

$\therefore \angle C={70}^{\circ }and\angle D={110}^{\circ }$

Hence $\angle B={110}^{\circ },\angle C={70}^{\circ }\angle D={110}^{\circ }$