Question

$\text{The diagonals AC and BD of a}\text{parallelogram ABCD intersect each other}\text{at the point O . If}\angle DAC={35}^{\circ }\text{and}\angle AOB={80}^{\circ },\text{then find the value of}\angle DBC.$

• A. ${55}^{\circ }$
• B. ${45}^{\circ }$
• C. ${75}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

$\text{Let}\angle DBC\text{be}x$.


$AD\parallel CB\text{and}AC\text{acts as the}\text{transversal.}\angle DAC=\angle ACB={35}^{\circ }(\because \text{Alternate interior angles are equal})$

$\text{In}△BOC,\text{by exterior angle property}\angle BCO+\angle OBC={80}^{\circ }{35}^{\circ }+x={80}^{\circ }x={80}^{\circ }-{35}^{\circ }x={45}^{\circ }$