Question

ABCD is a parallelogram in which $\angle ={110}^{\circ }$. Find the measure of each of the angles $\angle B,\angle Cand\angle D$.

Answer 1

In || gm ABCD,

$\angle A={110}^{\circ }$

But $\angle C=\angle A$ {Opposite angles of a || gm are equal}

$\therefore \angle ={110}^{\circ }$

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

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

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

But $\angle D=\angle B$ (Opposite angles)

$\therefore \angle D={70}^{\circ }$

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