11. If angle between two radii of a circle is 130°, the angle between the tangents at the ends of the radii i

Break Down the Problem

1. The problem involves a circle with two radii making an angle of 130° between them.
2. We need to find the angle between the tangents at the ends of these radii.

Relevant Concepts

1. The angle between the tangents at the ends of two radii can be found using the formula: $\text{Angle between tangents} = 180° - \frac{1}{2} \times \text{Angle between the radii}$

Analysis and Detail

1. Here, the angle between the radii is given as $130°$.
2. We can substitute this value into the formula: $\text{Angle between tangents} = 180° - \frac{1}{2} \times 130°$
3. Calculating $\frac{1}{2} \times 130°$: $\frac{1}{2} \times 130° = 65°$
4. Now substituting this value back into the equation: $\text{Angle between tangents} = 180° - 65° = 115°$

Verify and Summarize

• We double-checked the intermediate steps and the final calculation. The angle between the tangents was derived correctly.

Final Answer

The angle between the tangents at the ends of the radii is $115°$.