Question

ABCD is a parallelogram. Find the value of x in each case.

• A. ${45}^{\circ }$
• B. ${90}^{\circ }$
• C. ${40}^{\circ }$

Answer 1

Consecutive angles of a parallelogram are supplementary.
${110}^{\circ }+{25}^{\circ }+x={180}^{\circ }$
$\Rightarrow x={45}^{\circ }$

$\angle BCA=\angle DAC\text{(alternate interior angles)}\therefore \angle BCA={65}^{\circ }$
Similarly $\angle DBC={25}^{\circ }$
Thus $\angle BOC=x={180}^{\circ }-({65}^{\circ }+{25}^{\circ })={90}^{\circ }$


$\angle BOA={100}^{\circ }$(vertically opposite angles)
$\angle DBA={40}^{\circ }$(alternate interior angles)
Therefore $\angle BAO=x={180}^{\circ }-({100}^{\circ }+{40}^{\circ })={40}^{\circ }$