Mathematics

In the diagram above, PQ is a tangent at T to the circle ABT. ABC…

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.

  • A.
    20o
  • B.
    30o
  • C.
    35o
  • D.
    40o
  • E.
    50o
Correct Answer: Option E
Explanation

From the figure < TAB = < BTQ = 40° (alternate segment)

(therefore)< ATB = 180° – (70° + 40°) = 70° (angle on a straight line)

< BTC = (frac{40°}{2} = frac{< BTQ}{2})

(therefore < BTQ = 40°)

x° = 180° – (40° + 70° + 20°) 

= 50°