(a) The sides PQ and PR of \(\Delta\) PQR are produced to T and S respectively, such that TQR = 131^\circ and < QRS = 98^\circ. Find < QPR.
(b) The circumference of a circular track is 400m. Find its radius, correct to the nearest metre. [Take \(\pi = \frac{22}{7}\)]
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a)
< PQR = 180^\circ - 131^\circ = 49^\circ (angles on a straight line)
\(\therefore < PQR = 49^\circ\)
Also, \(< PQR = 180^\circ - 98^\circ = 82^\circ\)
\(\therefore < QPR = 180^\circ - (49^\circ + 82^\circ) = 180^\circ - 131^\circ\)
= \(49^\circ\)
(b) Circumference of the circular track = \(2\pi r\)
\(\therefore 2\pi r = 400 \)
where \(\pi = \frac{22}{7}\)
\(\therefore r = \frac{400 \times 1 \times 7}{22 \times 2} = \frac{700}{11}\)
= \(63.63m \approxeq 64m\)
Source: Myschool Past Questions Archive (Record #54595)