5 Marks Questions

Question 15 Marks

In the given figure, two straight line $PQ$ and $RS$ intersect at a $O$. If $\angle\text{POS} = 114^\circ, $ find the measure of each of the angles:

$i. \angle\text{POR}$
$ii. \angle\text{ROQ}$
$iii. \angle\text{QOS}$

Answer

$i. \angle\text{POS} +\angle\text{POR} = 180^\circ ($linear pair$)$
$114^\circ + \angle\text{POR}= 180^\circ $
$\angle\text{POR} = 180^\circ -114^\circ = 66^\circ$
$ii.$ Since $\angle\text{POS}$ and $\angle\text{QOR}$ are vertically opposite angles, they are equal.
$\therefore\angle\text{QOR} = 114^\circ$
$iii.$ Since $\angle\text{POR}$ and $\angle\text{QOS}$ are vertically opposite angles, they are equal.
$\therefore\angle\text{QOS} = 66^\circ$

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Question 25 Marks

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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MATHS 5 Marks Questions

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