Question

In parallelogram ABCD given below:If $\angle B=40°$, then find the value of
$\angle A,\angle Cand\angle D.$

• A. $\angle A=140°,\angle C=40°and\angle D=40°$
• B. $\angle A=140°,\angle C=40°and\angle D=140°$
• C. $\angle A=40°,\angle C=40°and\angle D=140°$
• D. $\angle A=140°,\angle C=140°and\angle D=40°$

Answer 1

The correct option is D $\angle A=140°,\angle C=140°and\angle D=40°$

In this figure,
Given that,
$\angle B=40°$.
We know that the opposite angles of a parallelogram are equal.
So, $\angle B=\angle D$
$\therefore \angle D=40°$
The sum of consecutive angles of a parallelogram is equal to 180°.
As, $\angle B$ and $\angle C$ are consecutive angles,
$\therefore \angle B+\angle C=180°$
$\Rightarrow 40°+\angle C=180°$
$\Rightarrow \angle C=180°-40°=140°$
$\angle Cand\angle A$ are opposite angles,
$\therefore \angle C=\angle A=140°$

Hence, the value of
$\angle A=140°,\angle C=140°and\angle D=40°.$