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WAEC Mathematics 2012 Question 23

Question 23

Angles and Polygons

In the diagram, MN, PQ, and RS are three intersecting straight lines. Which of the following statement(s) is/are true?
I. t = y
II. x + y + z + m = 180°
III. x + m + n = 180°
IV. x + n = m + z

Diagram for this question
  1. A.I and IV only
  2. B.II only
  3. C.III only
  4. D.IV only
Show the answer and explanation

Answer: C (III only)

Explanation

n = y (vertically opposite), and m + y + x = 180° (angles on the straight line MN). So x + m + n = 180° (III). t equals x, not y, so I is false; II and IV are also false.