In Figure, find x. Further find BOC, COD, and AOD - Vidyadip

Question

In Figure, find $\angle \text{x}.$ Further find $\angle \text{BOC}, \angle \text{COD}, \text{ and }\angle \text{AOD}$

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Answer

$\angle \text{AOD}+\angle \text{DOC}+\angle \text{COB}=180^\circ$ (Linear pair)
$(\text{x}+10)^\circ+\text{x}^\circ+(\text{x}+20)^\circ=180^\circ$
$3\text{x}+30^\circ=180^\circ$
$3\text{x}=180^\circ-30^\circ$
$3\text{x}=150^\circ$
$\text{x}=\frac{150^\circ}{3}=50^\circ$
$\angle \text{BOC}=\text{x}+20^\circ$
$=50^\circ+20^\circ=70^\circ$
$\angle \text{COD}=\text{x}=50^\circ$
$\angle \text{AOD}=\text{x}+10^\circ$
$=50^\circ+10^\circ=60^\circ$

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