Question

AB and CD are straight lines. $\angle AOC={40}^o,\angle COE={30}^o$. Find $\angle x$ and $\angle y$

• A. $\angle x={120}^o,\angle y={30}^o$
• B. $\angle x={110}^o,\angle y={40}^o$
• C. $\angle x={80}^o,\angle y={50}^o$
• D. $\angle x={90}^o,\angle y={60}^o$

Answer 1

The correct option is B $\angle x={110}^o,\angle y={40}^o$

Since, AB is a straight line and $\angle AOC+\angle COE+\angle BOE={180}^o$ (Angles on same sides of straight line)
${40}^o+{30}^o+\angle BOE={180}^o$
$\angle BOE={180}^o-{70}^o={110}^o$
$\angle x={110}^o$
Again, since CD is a straight line
So, $\angle COE+\angle BOE+\angle BOD={180}^o$ (Angle on same side of straight line)
${30}^o+{110}^o+\angle BOD={180}^o$
$\angle BOD={180}^o-{140}^o$
$\angle y={40}^o$