Question 41

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waecmaths question: 

Determine the value of m in the diagram

Option A: 

80o

Option B: 

90o

Option C: 

110o

Option D: 

150o

waecmaths solution: 

$\begin{align}  & \angle BAC+\angle DCB={{180}^{\circ }}\text{    }\!\!\{\!\!\text{ opp }\angle s\text{ of cyclic quad are supplementary }\!\!\}\!\!\text{ } \\ & \angle BAC={{180}^{\circ }}-{{80}^{\circ }}={{100}^{\circ }} \\ & Consider\text{ the triangle }BCD \\ & \angle DBC=\angle BDC\text{     }\!\!\{\!\!\text{ base angles of isso }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & x+x+{{80}^{\circ }}={{180}^{\circ }}\text{   }\!\!\{\!\!\text{ sum of }\angle s\text{ in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & x={{50}^{\circ }} \\ & \text{Consider triangle }ABD \\ & \angle ABC=\angle ADB\text{    }\!\!\{\!\!\text{ base }\angle s\text{ isso}\text{. }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & y+y+{{100}^{\circ }}={{180}^{\circ }}\text{   }\!\!\{\!\!\text{ sum of }\angle s\text{ in a }\vartriangle \text{ }\!\!\}\!\!\text{ } \\ & y={{40}^{\circ }} \\ & m=x+y={{50}^{\circ }}+{{40}^{\circ }}={{90}^{\circ }} \\\end{align}$

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