Question

If the angle between two radii of a circle is \( 120^\circ \), then the angle between the tangent and the ends of the radii is:

• A. \( 30^\circ \)
• B. \( 60^\circ \)
• C. \( 90^\circ \)
• D. \( 120^\circ \)

Hint:

The angle between the tangent and the radii is supplementary to the angle between the two radii.

Answer 1

The Correct Option is B

The angle between the two radii of the circle is given as \( 120^\circ \). We need to find the angle between the tangent and the ends of the radii. From geometry, we know that the angle between the tangent and a radius at the point of contact is \( 90^\circ \). The angle between the two radii and the tangent is the supplementary angle to the angle between the radii, which is: \[ \text{Angle between tangent and radii} = 180^\circ - 120^\circ = 60^\circ \] Thus, the angle between the tangent and the ends of the radii is \( 60^\circ \).