Question
If ABCD is a rhombus with $\angle\text{ABC}=56^\circ,$ find the measure of $\angle\text{ACD}.$
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Answer
The figure is given as follows:
ABCD is a rhombus. Therefore, ABCD is a parallelogram. Thus,$\angle\text{ABC}=\angle\text{ADC}$
$\angle\text{ADC}=56^\circ$ $[\angle\text{ABC}=56^\circ(\text{Given})]$
$\angle\text{ODC}=28^\circ$ $\Big[\angle\text{ODC}=\frac{1}{2}\angle\text{ADC}\Big]$
Now in $\triangle\text{ODC},$ we have:$\angle\text{OCD}+\angle\text{ODC}+\angle\text{COD}=180^\circ$
$\angle\text{OCD}+28^\circ+90^\circ=180^\circ$
$\angle\text{OCD}=62^\circ$
$\angle\text{ACD}=62^\circ$
Hence the measure of $\angle\text{ACD}$ is $62^\circ.$
ABCD is a rhombus. Therefore, ABCD is a parallelogram. Thus,$\angle\text{ABC}=\angle\text{ADC}$
$\angle\text{ADC}=56^\circ$ $[\angle\text{ABC}=56^\circ(\text{Given})]$
$\angle\text{ODC}=28^\circ$ $\Big[\angle\text{ODC}=\frac{1}{2}\angle\text{ADC}\Big]$
Now in $\triangle\text{ODC},$ we have:$\angle\text{OCD}+\angle\text{ODC}+\angle\text{COD}=180^\circ$
$\angle\text{OCD}+28^\circ+90^\circ=180^\circ$
$\angle\text{OCD}=62^\circ$
$\angle\text{ACD}=62^\circ$
Hence the measure of $\angle\text{ACD}$ is $62^\circ.$
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