Question

If $△$ $AOC$ $\cong$ $△$ $ODB$, then measure of $\angle$ $OBD$ is

• A. ${100}^o$
• B. ${50}^o$
• C. ${80}^o$
• D. None of these

Answer 1

The correct option is A ${100}^o$

In $△$ $OAC$, we have
$\angle$ $OAC$ $+$ $\angle$ $OCA$ $+$ $\angle$ $AOC$ $=$ ${180}^o$ (Angle sum property)
$\angle$ $OAC$ $+$ ${60}^o$ $+$ ${20}^o$ $=$ ${180}^o$
$\angle$ $OAC$ $=$ ${180}^o$ $-$ (${60}^o$ $+$ ${20}^o$) $=$ ${180}^o$ $-$ ${80}^o$ $=$ ${100}^o$
As $△$ $AOC$ $\cong$ $△$ $ODB$
Therefore, $\angle$ $OAC$ $=$ $\angle$ $OBD$ (By CPCT)
So, $\angle$ $OBD$ $=$ ${100}^o$