Home » » In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calcul...

# In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calcul...

### Question

In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/

A) 32 cm

B) 24 cm

C) 16 cm

D) 12 cm

### Explanation:

From the figure,
∠ XMN = ∠ XZY
Angle X is common
So, ∠ XNM = ∠ XYZ
Then from the angle relationship
$$\frac{XM}{XZ}$$ = $$\frac{XN}{XY}$$ = $$\frac{MN}{ZY}$$
XM = 8, XZ = 12 + 4 = 16,
XN = 12, XY = 8 + YM
$$\frac{8}{16}$$ = $$\frac{12}{(8 + YM) }$$
Cross multiply
8(8 + YM) = 192
64 + 8YM = 192
8YM = 128
YM = $$\frac{128}{8}$$
= 16cm

## Dicussion (1)

• From the figure,
∠ XMN = ∠ XZY
Angle X is common
So, ∠ XNM = ∠ XYZ
Then from the angle relationship
$$\frac{XM}{XZ}$$ = $$\frac{XN}{XY}$$ = $$\frac{MN}{ZY}$$
XM = 8, XZ = 12 + 4 = 16,
XN = 12, XY = 8 + YM
$$\frac{8}{16}$$ = $$\frac{12}{(8 + YM) }$$
Cross multiply
8(8 + YM) = 192
64 + 8YM = 192
8YM = 128
YM = $$\frac{128}{8}$$
= 16cm