Theory question 111
Angles and Polygons(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 the circle XYZ, ∠ZXO = 34° and ∠XOY = 146°. Find ∠OYZ.
Show the model answer
Model answer
(a) y = x + 7; exterior angles add to 360°
137 + x + (2x + 7) + (2x − 15) + (3x − x − 7) = 360 → 122 + 7x = 360
x = 34, y = 41
(b) ∠XZY = ½ × 146° = 73° (angle at centre)
OX = OZ → ∠OZX = 34°, so ∠OZY = 73° − 34° = 39°
OY = OZ → ∠OYZ = 39°
Explanation
Exterior angles of any polygon add up to 360°.