In the diagram, PQT is a straight line and SQ // RT.
(a) Join QR and show that : (i) < RPS = < QRT ; (ii) < PRS = < QTR.
(b) ABC is a triangle. The sides AB and AC are produced to D and E respectively such that < DBC = 132^\circ and < ECD = 96^\circ. Show that \(\Delta\) ABC is isosceles.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
(a) < QRT = < RQS (alternate angles)
< RPS = < RQS (angles in the same segment)
\(\therefore\) < RPS = < QRT
(ii) < QRT = < PQS (corresponding angles)
< PQS = < PRS (angles in the same segment)
\(\therefore\) < QTR = < PRS.
(b) \(< ABC = \hat{B} = 180^\circ - 132^\circ = 48^\circ\)
\(< ACB = \hat{C} = 180^\circ - 96^\circ = 84^\circ\)
\(< BAC = \hat{A} = 180^\circ - (48^\circ + 84^\circ) = 48^\circ\)
\(< BAC = < ABC = 48^\circ\)
\(\therefore \Delta ABC = isosceles\).
Source: Myschool Past Questions Archive (Record #53308)