Question

In the circle, reflex $\angle AOC=x^o,\angle ABC=y^o$. $OABC$ is a parallelogram, then find $y$.

• A. ${80}^o$
• B. ${120}^o$
• C. ${110}^o$
• D. Data insufficient

Answer 1

Answer: (B)

${120}^o$

In the circle, clearly, $x=2y$.

Then, $\angle AOC=360-x=360-2y$.

Here, $ABCD$ is a parallelogram

Then, $BCO+AOC={180}^o$
$\Rightarrow BCO+360-2y={180}^o$
$\Rightarrow 2y=BCO+{180}^o$.

Similarly, $ABC+BCO={180}^o$
$\Rightarrow y+2y-180=180$

$\Rightarrow 3y={360}^o$

$\Rightarrow y={120}^o$.

Hence, option $B$ is correct.