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Answer :
Final answer:
The angle between two tangents at the endpoints of the radii in a circle, where the angle between the radii is 110 degrees, is 70 degrees. This is calculated by subtracting the central angle and the right angles formed by the tangents and radii from the total circle angle of 360 degrees.
Explanation:
When considering the angle between two radii of a circle and the tangent lines at the ends of these radii, we must use our understanding of circle geometry and the properties of angles. The scenario involves a circle with a central angle of 110 degrees. The tangent lines at the endpoints of the radii create a geometrical figure that includes the radii, the tangents, and the angle between the tangents.
In circle geometry, a tangent to a circle is perpendicular to the radius at the point of tangency. Thus, each tangent forms a 90-degree angle with its respective radius. Given that the angle between the two radii is 110 degrees and we have two right angles formed by each tangent with the radius, we can find the angle between the two tangents by subtracting the central angle from 360 degrees - the total degrees in a full revolution around a circle - and then subtracting the angles created by the radii.
Here is the calculation step by step:
- Start with the full angle of a circle which is 360 degrees.
- Subtract the angle between the radii, which is 110 degrees, from the full angle. This leaves us with 250 degrees.
- Because there are two places where the tangents intersect the radii, we have two right angles (90 degrees each). Subtract these from the remaining angle (250 degrees - 2*90 degrees).
- The final step is the calculation 250 degrees - 180 degrees, which equals 70 degrees.
This means the angle between the two tangents is 70 degrees.
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