In the diagram above, PQ is a tangent at T to the circle ABT. ABC is a straight line and TC bisects ∠BTO. Find x.
Attached Figure / Diagram
A
20o
B
30o
C
35o
D
40o
E
50o
Verified Correct Answer: E.
Step-by-Step Mathematical Solution
From the figure < TAB = < BTQ = 40^\circ (alternate segment)
\(\therefore\)< ATB = 180^\circ - (70^\circ + 40^\circ) = 70^\circ (angle on a straight line)
< BTC = \(\frac{40^\circ}{2} = \frac{< BTQ}{2}\)
\(\therefore < BTQ = 40^\circ\)
x^\circ = 180^\circ - (40^\circ + 70^\circ + 20^\circ)
= 50^\circ
Source: Myschool Past Questions Archive (Record #22687)