Question

If $ABCD$ is a rectangle with $\angle BAC={32}^{\circ },$ find the measure of $\angle DBC.$

Answer 1

In rectangle $ABCD,\angle BAC={32}^{\circ }$.

Diagonals bisect each other at $O.$

$\because OA=OB$

$\therefore \angle OBA(=\angle DBA)=\angle BAC={32}^{\circ }$ [Angles opposite to equal sides are equal]

But $\angle ABC={90}^{\circ }$ (Angle of a rectangle)

$\therefore \angle DBC=\angle ABC-\angle DBA$

$={90}^{\circ }-{32}^{\circ }={58}^{\circ }$