Question

11(a) The exterior angles of a polygon are 42°, 38°, 57°, x°, (x+y)°, (2x−15)° and (3x−y)°. If x is 7° less than y, find the values of x and y.
(b) In the diagram, O is the centre of circle XYZ, ∠ZXO=34° and ∠XOY=146°. Find ∠OYZ.

Accepted Answer

(a) Since the sum of exterior angles of a polygon = 360°:
42+38+57+x+(x+y)+(2x−15)+(3x−y) = 360
122+7x = 360
7x=238
x=34°
From the second statement, y−x=7, so y=x+7=34+7=41°.

(b) To find ∠OYZ:
∠XZY = ½(146°) = 73° (angle at centre equals twice angle at circumference, so angle at circumference = ½ angle at centre)
Since OZ=OX (radii), ∠OZX=34° (base angle of isosceles triangle)
∠OZY=73°−34°=39° (base angle of isosceles triangle OZY)
∠OYZ=∠OZY=39° (base angles of isosceles triangle OYZ are equal, since OZ=OY radii).

WAEC Mathematics 2022 Theory — Question 11

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