JAMB 1985 · UME · Q49

In the figure, find the angle xx.

20°80°40°x°
Worked solution (try it first)
  1. The interior angles of a quadrilateral add up to 360∘360^\circ.
  2. The three marked angles add up to 20∘+80∘+40∘=140∘20^\circ + 80^\circ + 40^\circ = 140^\circ.
  3. So the interior angle at the inward-pointing vertex is 360∘−140∘=220∘360^\circ - 140^\circ = 220^\circ, a reflex angle.
  4. xx is the angle on the other side of that vertex, and angles at a point add up to 360∘360^\circ: x=360∘−220∘=140∘x = 360^\circ - 220^\circ = 140^\circ, option E.

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