Theory question 104
Angles and Polygons(a) The sides PQ and PR of ΔPQR are produced to T and S respectively, such that ∠TQR = 131° and ∠QRS = 98°. Find ∠QPR.
(b) The circumference of a circular track is 400m. Find its radius, correct to the nearest metre (Take π = 22/7).
Show the model answer
Model answer
(a) ∠PQR = 180° − 131° = 49° (angles on a straight line)
∠PRQ = 180° − 98° = 82° (angles on a straight line)
∠QPR = 180° − (49° + 82°) = 49° (angles in a triangle)
(b) 2πr = 400, so r = 400 × 7 ÷ (2 × 22) = 63.6
r ≈ 64 m (nearest metre)
Explanation
Each exterior angle and its interior angle add up to 180°.