(a) The sides PQ and PR of (Delta) PQR 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 (pi = frac{22}{7})]
Explanation
(a)
< PQR = 180° – 131° = 49° (angles on a straight line)
(therefore < PQR = 49°)
Also, (< PQR = 180° – 98° = 82°)
(therefore < QPR = 180° – (49° + 82°) = 180° – 131°)
= (49°)
(b) Circumference of the circular track = (2pi r)
(therefore 2pi r = 400 )
where (pi = frac{22}{7})
(therefore r = frac{400 times 1 times 7}{22 times 2} = frac{700}{11})
= (63.63m approxeq 64m)