To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at endpoints of those two radii of the circle, the angle between them should be

Construction:

In the given figure:

OP and OQ are the tangents to the circle.

Now,

Sum of opposite angles = 180°

∴ POQ + PRQ=180°

⇒ 60° + θ=180°

⇒ θ=120°

Hence, the angle between them should be 120°.

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