JAMB 1991 · UME · Q37

In the figure, the two horizontal lines are parallel. Find the value of yy.

152°30°y
Worked solution (try it first)
  1. Angles on a straight line at the bend: the upper slanted segment makes 180∘−152∘=28∘180^\circ - 152^\circ = 28^\circ with the horizontal.
  2. Draw a horizontal line through the apex.
  3. By alternate angles the upper segment makes 28∘28^\circ with it, so the downward segment makes 28∘+30∘=58∘28^\circ + 30^\circ = 58^\circ with it.
  4. By alternate angles again, the downward segment makes 58∘58^\circ with the lower line on its right-hand side.
  5. yy is on the left, so y=180∘−58∘=122∘y = 180^\circ - 58^\circ = 122^\circ, option B.

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