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In the diagram, < QPR = 60o < PQR = 50o < QRS = 2xo...

Mathematics
WAEC 2008

In the diagram, < QPR = 60o

< PQR = 50o

< QRS = 2xo

< SRP = 3xo

< UQP = yo and RS//TU

calculate y
  • A. 102o
  • B. 78o
  • C. 70o
  • D. 60o
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Correct Answer: Option A
Explanation
< RQT = < QRS = 2x (Alternate angles). But in \(\bigtriangleup\) PRQ

50 + 60 + (2x + 3x) = 180o(Angles in a triangle)

110 + 5x = 180o

5x = 180o - 110 = 70o

x = \(\frac{70}{5}\) = 14o

Also y + 50 + 2(14) = 180o

y + 50 + 28 = 180o

y = 180 - 78

y = 102o

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