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JAMB 1997 · UME · Q25

Each of the base angles of an isosceles triangle is 58∘58^\circ and all the vertices lie on a circle. Determine the angle which the base of the triangle subtends at the centre of the circle.

Worked solution (try it first)
  1. The angles of the triangle add up to 180∘180^\circ, so the apex angle is 180∘−58∘−58∘=64∘180^\circ - 58^\circ - 58^\circ = 64^\circ.
  2. The base is opposite the apex, so the apex angle is the angle the base makes at the circumference.
  3. The angle at the centre is twice that: 2×64∘=128∘2 \times 64^\circ = 128^\circ, option A.

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