Multiple choice

If the angle between two radii of a circle is $100^{\circ}$, the angle between the tangents at the ends of those radii is :

  1. $50^{\circ}$
  2. $60^{\circ}$
  3. $80^{\circ}$
  4. $90^{\circ}$
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C Correct answer
Explanation

The angle between the tangents is supplementary to the angle between the radii. 180 - 100 = 80 degrees.

AI explanation

The radii and the two tangents form a quadrilateral where the two angles between the radii and their respective tangents are 90 degrees each. Since the sum of the interior angles of any quadrilateral is 360 degrees, the sum of the remaining two angles equals 360 degrees minus 180 degrees, which is 180 degrees. Subtracting the given central angle of 100 degrees from 180 degrees gives the angle between the tangents as 80 degrees.

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