Question

In the adjoining figure, TS is a tangent to a circle with centre O. The value of 2x° is:

Options

• 22.5

• 45

• 67.5

• 90

Answer 1

45

Explanation:

We know that, ∠OST = 90°  ....(r ⊥ T)

In ΔOST,

Sum of the internal angles of any triangle is 180°.

x° + 3x° + 90° = 180°

4x° = 90°

x° = `90/4`

x° = 22.5°

⇒ 2x = 2 × 22.5

= 45°