2018

Mathematics

JAMB

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

Correct Answer: 16 cm

Explanation

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

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

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