Question

$ABCD$ is a rhombus with $ABC={56}^o$, then $\angle ACD$ will be

• A. ${56}^o$
• B. ${124}^o$
• C. ${62}^o$
• D. ${34}^o$

Answer 1

The correct option is C ${62}^o$

Consecutive angles of a rhombus are supplementary.

$\therefore$ $\angle ABC+\angle BCD={180}^O$

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

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

$\therefore$ $\angle BCD={124}^o$

Diagonal $AC$ bisect $\angle BCD$

$\therefore$ $\angle ACD=\frac{\angle BCD}{2}=\frac{{124}^o}{2}={62}^o$

$\therefore$ $\angle ACD={62}^o$.