Question

ABCD is a paralleologram in which diagonal AC bisects $\angle BAD.$ If $\angle BAC={35}^{\circ }$, then $\angle ABC=$

• A. ${70}^{\circ }$
• B. ${110}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is B

${110}^{\circ }$

In || gm ABCD, AC is its diagonal which bisects $\angle BAD$.

$\therefore \angle BAD=2\times {35}^{\circ }={70}^{\circ }But\angle A+\angle B={180}^{\circ }\left(\text{Sum of consecutive angles}\right)\Rightarrow {70}^{\circ }+\angle B={180}^{\circ }\Rightarrow \angle B={180}^{\circ }-{70}^{\circ }\therefore \angle B={110}^{\circ }\Rightarrow ABC={110}^{\circ }$