Question
In the figure given alongside, find:
- $\angle\text{ACD}$
- $\angle\text{ADC}$
- $\angle\text{DAE}$
✓
Answer
- In $\triangle\text{ABC},$ sides BC is produced to D and BA to E.
$\angle\text{ACB} +\angle\text{ACD} = 180^\circ$ (Linear pair)
$\Rightarrow100^\circ+\angle\text{ACD} = 180^\circ$
$\Rightarrow\angle\text{ACD} = 180^\circ-100^\circ=80^\circ$
- In $\triangle\text{ABC},$
$\Rightarrow50^\circ+80^\circ+\angle\text{ADC} = 180^\circ$
$\Rightarrow130^\circ+\angle\text{ADC}=180^\circ$
$\Rightarrow\angle\text{ADC}=180^\circ-130^\circ=50^\circ$
- Now, in $\triangle\text{ABD},$ BA is produced to E.
Hence, $\angle\text{ACD}=80^\circ,\angle\text{ADC}=50^\circ$and $\angle\text{DAE}=130^\circ$
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