Question

In fig. ABCD is a rhombus with $\angle ABC={56}^o$. Determine $\angle ACD$

• A. ${62}^o$
• B. ${52}^o$
• C. ${68}^o$
• D. none of the above

Answer 1

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

$ABCD$ is a rhombus
$\Rightarrow ABCD$ is a parallelogram
$\Rightarrow \angle ABC=\angle ADC$ [Opp $\angle s$ of ${\parallel }_{gm}$ are equal]
$\Rightarrow \angle ADC={56}^o[\because \angle ABC={56}^o(Given\left)\right]$
$\Rightarrow \angle ODC={28}^o[\because \angle ODC=\frac{1}{2}\angle ADC]$
Now, in $\Delta OCD$, we have
$\angle OCD+\angle ODC+\angle COD={180}^o$
$\Rightarrow \angle OCD+{28}^o+{90}^o={180}^o$
$\Rightarrow \angle OCD={62}^o$
$\Rightarrow \angle ACD={62}^o$