Question

Can someone help me solve this?

Answer 1

Answer:

∠ ABC = 22°

Step-by-step explanation:

OA = OB ( radii of circle )

Then Δ OAB is isosceles with base angles congruent , that is

∠ OBA = ∠ OAB = 17x

The sum of the 3 angles in the triangle sum to 180°

17x + 17x + 11x = 180

45x = 180 ( divide both sides by 45 )

x = 4

Then

∠ OBA = 17x = 17(4) = 68°

BC is a tangent so ∠ OBC = 90°

∠ ABC = 90° - ∠ OBA = 90° - 68° = 22°