Home » Past Questions » Mathematics » 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/

Options

A) 32 cm

B) 24 cm

C) 16 cm

D) 12 cm

The correct answer is 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


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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

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