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WAEC Mathematics 1997 Question 25

Question 25

Triangles and Quadrilaterals

From the diagram below, which of the following is true?

Diagram for this question
  1. A.a + b + x = 180
  2. B.a = b + x
  3. C.a − b = 180 − x
  4. D.a + b = x + 180
  5. E.a − b = x − 180.
Show the answer and explanation

Answer: D (a + b = x + 180)

Explanation

The top interior angle is 180 − a. The exterior angle b equals the sum of the two opposite interior angles: b = x + (180 − a), so a + b = x + 180.