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Answer :
Final answer:
If two radii of a circle form an angle of 130 degrees, then the angle between the tangents at the end of these radii is 280 degrees.
Explanation:
When two radii of a circle form an angle of 130 degrees, the angle between the tangents at the end of these radii follows a specific mathematical rule. This rule is derived from the properties of a circle and angles within the circle.
The rule states that if an angle (θ) is formed by two radii in a circle, the tangent lines at the points where the radii hit the circumference will make an angle of 180 degrees minus twice the angle θ. In this case, θ is 130, so the angle between the tangents is 180 - 2*130 = -80 degrees.
However, an angle of -80 degrees might seem unusual. This is because the tangents form an angle that extends 'outside' the circle, creating a reflex angle. To describe this in a more usual way, we could say that the angle between the tangents is 360 + (-80) = 280 degrees.
In conclusion, the angle between the tangents at the end of the radii is 280 degrees.
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