Home » » In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54$$^{\circ}$$ ...

# In the figure above, KL//NM, LN bisects < KNM. If angles KLN is 54$$^{\circ}$$ ...

### Question

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.

### Options

A) 91$$^{\circ}$$

B) 89$$^{\circ}$$

C) 37$$^{\circ}$$

D) 19$$^{\circ}$$

### Explanation:

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 $$\bigtriangleup$$)

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

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

= 37$$^{\circ}$$

## Discussion (2)

• 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 $$\bigtriangleup$$)

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

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

= 37$$^{\circ}$$