# Question 25

Jambmaths question:

The value of x in the figure above is

Option A:

130o

Option B:

110o

Option C:

100o

Option D:

70o

Jamb Maths Solution:

\begin{align} & \text{Draw a line }AB\text{ passing R},\text{ parallel }PQ\text{ and }TS,\text{ Also produce }PQ\text{ and }TS~\text{to }D \\ & P\overset{\wedge }{\mathop{Q}}\,R+C\overset{\wedge }{\mathop{Q}}\,R={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ Sum of angles on a straight line }\!\!\}\!\!\text{ } \\ & \text{14}{{\text{0}}^{\circ }}+C\overset{\wedge }{\mathop{Q}}\,R={{180}^{\circ }} \\ & C\overset{\wedge }{\mathop{Q}}\,R={{40}^{\circ }} \\ & A\overset{\wedge }{\mathop{R}}\,Q=C\overset{\wedge }{\mathop{Q}}\,R={{40}^{\circ }}\text{ }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & T\overset{\wedge }{\mathop{S}}\,R+R\overset{\wedge }{\mathop{S}}\,D={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ Sum of angles on straight line }\!\!\}\!\!\text{ } \\ & R\overset{\wedge }{\mathop{S}}\,D={{180}^{\circ }}-{{120}^{\circ }}={{60}^{\circ }} \\ & A\overset{\wedge }{\mathop{R}}\,S=R\overset{\wedge }{\mathop{S}}\,D={{60}^{\circ }}\text{ }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & A\overset{\wedge }{\mathop{R}}\,Q+A\overset{\wedge }{\mathop{R}}\,S=x={{40}^{\circ }}+{{60}^{\circ }}={{100}^{\circ }} \\ & \text{Alternative method} \\ & P\overset{\wedge }{\mathop{Q}}\,R+Q\overset{\wedge }{\mathop{R}}\,S+R\overset{\wedge }{\mathop{S}}\,T={{360}^{\circ }} \\ & {{140}^{\circ }}+Q\overset{\wedge }{\mathop{R}}\,S+{{120}^{\circ }}={{360}^{\circ }} \\ & Q\overset{\wedge }{\mathop{R}}\,S={{360}^{\circ }}-{{260}^{\circ }}={{100}^{\circ }} \\\end{align}

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