Question

Consider the figure given below:

If $△BOC\cong △AOD$ and $\angle DOA={30}^{\circ }$, then what is the measure of $\angle BCO$?

• A. 60${}^{\circ }$
• B. 30${}^{\circ }$
• C. 50${}^{\circ }$
• D. 40${}^{\circ }$

Answer 1

The correct option is A 60${}^{\circ }$

Given, $△BOC\cong △AOD$

In $△BOC$ and $△AOD$,
$\angle COB=\angle DOA={30}^{\circ }$ .... (Corresponding parts of congruent triangle)
$\angle OBC={90}^{\circ }$ ..... (Given)

$\angle BCO+\angle COB+\angle OBC={180}^{\circ }$ .... (Angle sum property of a triangle)

$\angle BCO={180}^{\circ }-(\angle COB+\angle OBC)$
$\Rightarrow \angle BCO={180}^{\circ }-({30}^{\circ }+{90}^{\circ })$
$\Rightarrow \angle BCO={180}^{\circ }-{120}^{\circ }$
$\Rightarrow \angle BCO={60}^{\circ }$