Question

$ABCD$ is a rhombus. If $\angle BCA={35}^o$, find $\angle ADC$.

Answer 1

Given: Rhombus $ABCD$ in which $\angle BCA={35}^o$

To find: $\angle ADC$

Proof: $AD\parallel BC$

$\angle DAC=\angle BCA$ (Alternate $\angle S$)

But $\angle BCA={35}^o$ (given)

$\angle DAC={35}^o$

But $\angle DAC=\angle ACD(AD=CD)$ and $\angle DAC=\angle ADC={180}^o$

$\angle B^o+{35}^o+\angle ACD={180}^o$

$\angle ADC={180}^o-{70}^o={110}^o$

Hence $\angle ADC={110}^o$