Question

In a quadrilateral ABCD, $\angle A+\angle C={180}^{\circ }$ then $\angle B+\angle D=$

• A. ${360}^{\circ }$
• B. ${100}^{\circ }$
• C. ${180}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is C ${180}^{\circ }$

We have,
$\angle A+\angle B+\angle C+\angle D={360}^{\circ }$
$(\angle A+\angle C)+(\angle B+\angle D)={360}^{\circ }$
${180}^{\circ }+(\angle B+\angle D)={360}^{\circ }$
$\angle B+\angle D={180}^{\circ }$