Question

If ABCD is a rhombus with $\angle ABC={56}^{\circ }$, find the measure of $\angle ACD$.

Answer 1

In rhombus ABCD,

Diagonals bisect each other at O at right angles.

$\angle ABC={56}^{\circ }$

But $\angle ABC+\angle BCD={180}^{\circ }$ (Sum of consecutive angles)

$\Rightarrow {56}^{\circ }+\angle BCD={180}^{\circ }$

$\Rightarrow \angle BCD={180}^{\circ }-{56}^{\circ }={124}^{\circ }$

$\because$Diagonals of a rhombus bisect the opposite angle

$\therefore \angle ACD=\frac{1}{2}\angle BCD=\frac{1}{2}\times {124}^{\circ }$

= ${62}^{\circ }$