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WAEC Mathematics 2011 Question 27

Question 27

Triangles and Quadrilaterals

From the diagram, which of the following statements are true?
I. m = q
II. n = q
III. n + p = 180°
IV. p + m = 180°

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

Answer: B (I and IV)

Explanation

MNQP is a parallelogram (both pairs of sides parallel). Opposite angles are equal, so m = q (I), and neighbouring angles add to 180°, so p + m = 180° (IV).