Theory question 104
Angles and Polygons(a) A pentagon is such that one of its exterior angles is 60°. Two others are (90 − m)° each while the remaining angles are (30 + 2m)° each. Find the value of m.
(b) In the diagram, PQR is a straight line, QR = √3 cm and SQ = 2 cm. Calculate, correct to one decimal place, ∠PQS.
Show the model answer
Model answer
(a) Exterior angles add to 360°: 60 + 2(90 − m) + 2(30 + 2m) = 360 → 300 + 2m = 360 → m = 30.
(b) In right-angled ΔSQR (right angle at R): cos ∠SQR = √3/2, so ∠SQR = 30°.
∠PQS = 180° − 30° = 150.0°.
Explanation
The exterior angles of any polygon add up to 360°.