In the given figure, two straight line AB and CD intersect at a p… - Vidyadip

Question

In the given figure, two straight line $AB$ and $CD$ intersect at a point $O$. If $\angle\text{AOC} = 42^\circ,$ find the measure of each of the angles:

$i. \angle\text{AOD}$
$ii. \angle\text{BOD}$
$iii. \angle\text{COB}$

✓

Answer

$AB$ and $CD$ intersect at $O$ and $CD$ is a straight line.
$i. \angle\text{COA}+ \angle\text{AOD}= 180^\circ ($linear pair$)$
$42^\circ+ \angle\text{AOD} = 180^\circ$
$\angle\text{AOD} = 138^\circ$
$ii. \angle\text{COA}$ and $\angle\text{BOD}$ are vertically opposite angles.
$\therefore\angle\text{COA} = \angle\text{BOD} = 42^\circ [$from $(i)]$
$iii. \angle\text{COB}$ and $\angle\text{AOD}$ are vertically opposite angles.
$\therefore\angle\text{COB} = \angle\text{AOD} = 138^\circ [$from $(ii)]$

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