4 Mark Question

Question 14 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:

Answer

$114^\circ + \angle\text{POR}= 180^\circ $
$\angle\text{POR} = 180^\circ -114^\circ = 66^\circ$

Since $\angle\text{POS}$ and $\angle\text{QOR}$ are vertically opposite angles, they are equal.

$\therefore\angle\text{QOR} = 114^\circ$

Since $\angle\text{POR}$ and $\angle\text{QOS}$ are vertically opposite angles, they are equal.

$\therefore\angle\text{QOS} = 66^\circ$

Question 24 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:

Answer

AB and CD intersect at O and CD is a straight line.

$42^\circ+ \angle\text{AOD} = 180^\circ$

$\angle\text{AOD} = 138^\circ$

$\therefore\angle\text{COA} = \angle\text{BOD} = 42^\circ$ [from (i)]

$\therefore\angle\text{COB} = \angle\text{AOD} = 138^\circ$ [from (i)]

Maths 4 Mark Question