Question

10. Using ruler and a pair of compasses only,
(a) Construct: (i) ΔXYZ such that |XY|=10cm, ∠XYZ=30° and ∠YXZ=45° (ii) locus l1, of points equidistant from Y and Z; (iii) locus l2, of point of intersection of l1 and l2.
(b) Locate point M, the point of intersection of l1 and l2.
(c) Measure ∠ZMY

Accepted Answer

Construction procedure:
(a)(i) Draw a straight line XY = 10cm long.
(ii) At X, construct an angle of 45° (∠YXZ=45°) using compass and ruler (bisect a 90° angle to get 45°).
(iii) At Y, construct an angle of 30° (∠XYZ=30°) using compass and ruler (bisect a 60° angle to get 30°).
The intersection of the two rays from X and Z gives point Z, completing triangle XYZ.

(a)(ii) l1: Bisect line YZ perpendicularly (the perpendicular bisector of YZ) — this is the locus of points equidistant from Y and Z.

(a)(iii) l2: Construct a line parallel to XY, passing through Z, at 90° to line XY (perpendicular to XY through Z, or as otherwise specified) — this is the second locus.

(b) M is located at the point where locus l1 (perpendicular bisector of YZ) intersects locus l2.

(c) By construction and measurement, ∠ZMY = 120° (this is obtained by actual measurement with a protractor after accurate construction).

WAEC Mathematics 2016 Theory — Question 10

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