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.

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

Question 1 Report

^{\circ}

^{\circ}

^{\circ}

^{\circ}

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 $^{\circ}$

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.