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In the diagram, PQ//RS. Find x in terms of y and z

Mathematics
WAEC 2018

In the diagram, PQ//RS. Find x in terms of y and z

  • A. x = 240\(^o\) - y - z
  • B. x = 180\(^o\) - y - z
  • C. x = 360\(^o\) + y -z
  • D. x = 360\(^o\) - y - z
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Correct Answer: Option D
Explanation

In the diagram,

a = z (alternate angles)

b = 180\(^o\) - a (angles on a straight line)

b = 180\(^o\) - z

c = 180\(^o\) - x (angles on a straight line)

y = b + c (sum of oposite interior angles)

y = 180\(^o\) - z + 180\(^o\) - x

y = 360\(^o\) - z - x

x = 360\(^o\) - y - z

 


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