passwella.
Menu

JAMB Mathematics 1999 Question 28

Question 28

Circle Theorems

In the diagram above, EFGH is a cyclic quadrilateral in which EH||FG, EG and FH are chords. If ∠FHG = 42° and ∠EFH = 34°, calculate ∠HEG.

Diagram for this question
  1. A.34°
  2. B.42°
  3. C.52°
  4. D.76°
Show the answer and explanation

Answer: C (52°)

Explanation

∠EGH = ∠EFH = 34° (same segment). Let ∠HEG = y; then ∠HFG = y (same segment) and ∠EHF = y (alternate angles, EH ∥ FG). In triangle EHG: y + (y + 42°) + 34° = 180°, so y = 52°.