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JAMB Mathematics 1984 Question 49

Question 49

Constructions

Use the construction (Fig. 1) to answer this question. What is the obtuse angle formed when the point U is joined to Q?

Diagram for this question
  1. A.75°
  2. B.145°
  3. C.120°
  4. D.105°
  5. E.125°.
Show the answer and explanation

Answer: D (105°)

Explanation

QT is the perpendicular to PQ at Q (90°). The arcs through T and S bisect a further angle, putting QU 15° beyond QT, so the obtuse angle PQU is 90° + 15° = 105°.