Question

In a trapezium ABCD, $AB||CD$ and ∠A = ∠B = 40°. Compute ∠C + ∠D.

• A. 280°
• B. 140°
• C. 70°
• D. 40°

Answer 1

The correct option is A 280°

In the figure given below, $AB||CD$ and ∠A = ∠B = 40°.
Now,
$\angle C+\angle B=180°\text{∠C \& ∠B are co-interior angle. So, there sum will 180°}$
$\angle C+40°=180°(\because \angle B=40°)$
$⟹\angle C=180°-40°=140°$

And
$\angle A+\angle D=180°\text{(∠A \& ∠D are co-interior angle. So, there sum will 180°}$
$\angle D+40°=180°(\because \angle A=40°)$
$⟹$$\angle D=180°-40°=140°$

We have to find ∠C + ∠D,
$⟹\angle C+\angle D=140°+140°=280°$

Hence, option A is correct.