Question 25

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Jambmaths question: 

In the diagram above $PQ\parallel RS$, the size of the angle marked x is

Option A: 

100o

Option B: 

80o

Option C: 

50o

Option D: 

30o

Jamb Maths Solution: 

$\begin{align}  & F\overset{\wedge }{\mathop{B}}\,D=A\overset{\wedge }{\mathop{B}}\,P={{30}^{\circ }}\text{  (vertically opposite angles)} \\ & \text{consider }\Delta BDF \\ & F\overset{\wedge }{\mathop{B}}\,D+B\overset{\wedge }{\mathop{D}}\,F+B\overset{\wedge }{\mathop{F}}\,D=\text{ (sum of }\angle \text{s in a }\Delta \text{)} \\ & {{50}^{\circ }}+{{30}^{\circ }}+B\overset{\wedge }{\mathop{F}}\,D={{180}^{\circ }} \\ & B\overset{\wedge }{\mathop{F}}\,D= \\ & B\overset{\wedge }{\mathop{F}}\,D+Q\overset{\wedge }{\mathop{F}}\,D=\text{ (sum of }\angle \text{s on a straight line)} \\ & {{100}^{\circ }}+Q\overset{\wedge }{\mathop{F}}\,D={{180}^{\circ }} \\ & x=Q\overset{\wedge }{\mathop{F}}\,D={{80}^{\circ }} \\\end{align}$

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