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.

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.

Answer Details

In the diagram above, $\alpha$ = 54${}^{\circ }$(alternate angles; KL||MN) < KNM = 2$\alpha$ (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${}^{\circ }$