Multiple choice

If the length of a minor arc $\widehat { AB } $ of a circle is $\cfrac{1}{4}$ of its circuference, then the angle subtended by the minor arc $\widehat { AB } $ at the center will be

  1. $30$
  2. $45$
  3. $90$
  4. $60$
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C Correct answer
Explanation

The circumference of a circle corresponds to 360 degrees. If an arc is 1/4 of the circumference, the angle subtended at the center is 1/4 of 360 degrees, which is 90 degrees.

AI explanation

The minor arc makes up one-fourth of the total circumference, meaning its proportion of the full 360-degree circle is 1 divided by 4. By multiplying this fraction by 360, we calculate the angle subtended at the center, yielding 360 divided by 4. The result is 90 degrees.

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