Question

Find value of X if TN is tangent

Answer 1

Answer:

30°

Step-by-step explanation:

∠OTN is a right angle since it's where a radius meets a tangent

∠NOT = 60°  since the angles in triangle NOT add up to 180°

Triangle ABO is isosceles since OB and OA are radii

=> ∠OBA = ∠OAB       .... (1)

∠NOT is exterior angle of triangle ABO

=> ∠NOT = ∠OBA + ∠OAB = 2 × ∠OBA         [ using equation (1) ]

=> x = ∠OBA = (1/2) ∠NOT = (1/2) × 60° = 30°