In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and XMN = XZY. Calculate /YM/
A. 32cm
B. 24 cm
C. 16 cm
D. 12 cm
Correct Answer: C
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