Question
In the adjoining figure, three coplanar lines AB, CD and EF intersect at a point O. Find the value of x. Also, find $\angle\text{AOD},\angle\text{COE}$ and $\angle\text{AOE}.$
✓
Answer
We know that if two lines intersect, then the vertically-opposite angles are equal.$\therefore\angle\text{DOF}=\angle\text{COE}=5\text{x}^\circ$
$\angle\text{AOD}=\angle\text{BOC}=2\text{x}^\circ\text{ and}$
$\angle\text{AOE}=\angle\text{BOF}=3\text{x}^\circ$
Since, AOB is a straight line, we have:$\angle\text{AOE}+\angle\text{COE}+\angle\text{BOC}=180^\circ$
⇒ 3x + 5x + 2x = 180º ⇒ 10x = 180º ⇒ x = 18º Therefore,$\angle\text{AOD}=2\times18^\circ=36^\circ$
$\angle\text{COE}=5\times18^\circ=90^\circ$
$\angle\text{AOE}=3\times18^\circ=54^\circ$
$\angle\text{AOD}=\angle\text{BOC}=2\text{x}^\circ\text{ and}$
$\angle\text{AOE}=\angle\text{BOF}=3\text{x}^\circ$
Since, AOB is a straight line, we have:$\angle\text{AOE}+\angle\text{COE}+\angle\text{BOC}=180^\circ$
⇒ 3x + 5x + 2x = 180º ⇒ 10x = 180º ⇒ x = 18º Therefore,$\angle\text{AOD}=2\times18^\circ=36^\circ$
$\angle\text{COE}=5\times18^\circ=90^\circ$
$\angle\text{AOE}=3\times18^\circ=54^\circ$
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