In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54? ? and angle MKN is 35? ? , calculate the size of angle KMN.

Assessment: JAMB UTME - Mathematics - 2014 Subject: General Mathematics

Question 1 Report

In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54 $^{\circ}$ and angle MKN is 35 $^{\circ}$ , calculate the size of angle KMN.

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Answer Details

In the diagram above, $α$ = 54 $^{\circ}$ (alternate angles; KL||MN) < KNM = 2 $α$ (LN is bisector of < KNM) = 108 $^{\circ}$

35 $^{\circ}$ + < KMN + 108 $^{\circ}$ = 180 $^{\circ}$ (sum of angles of $△$ )

< KMN + 143 $^{\circ}$ = 180 $^{\circ}$

< KMN = 180 $^{\circ}$ - 143 $^{\circ}$

= 37 $^{\circ}$

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