Question 27

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waecmaths question: 

From the diagram, which of the following statement are true?

I.  m = q

II. n = q

III.n + p =180o

IV. p + m =180o

Option A: 

I and III

Option B: 

 I and IV

Option C: 

II and III

Option D: 

 II and IV

waecmaths solution: 

$\begin{align}  & \angle NMP=\angle QPA=m\text{   }\!\!\{\!\!\text{ corresponding }\angle \text{s }\!\!\}\!\!\text{ } \\ & \angle QPA+\angle MPQ=m+p={{180}^{\circ }}\text{ }\!\!\{\!\!\text{ }\angle \text{s on a st}\text{.line }\!\!\}\!\!\text{ } \\ & \angle PQB=\angle MNQ=n\text{   }\!\!\{\!\!\text{ corresponding }\angle \text{s }\!\!\}\!\!\text{ } \\ & \angle PQB+\angle NQP=n+q\text{  }\!\!\{\!\!\text{ }\angle \text{s on a st}\text{.line }\!\!\}\!\!\text{ } \\ & \angle PQB=\angle MPQ\text{    }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ } \\ & i.e.\text{ }n=p \\ & \angle NQP=\angle QPA\text{   }\!\!\{\!\!\text{ alternate angles }\!\!\}\!\!\text{ } \\ & i.e.\text{ }m=p \\\end{align}$From the above only II and IV satisfies the options given. The correct option is D

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