Multiple choice

In a circle, two arc of unequal length subtended angles in the ratio $5: 3$. If the smaller angle is $45^o,$ then the measure of other angle is:

  1. $75^o$
  2. $72^o$
  3. $60^o$
  4. $78^o$
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A Correct answer
Explanation

The ratio of angles is 5:3. If the smaller angle (3 parts) is 45 degrees, then 1 part = 15 degrees. The other angle (5 parts) = 5 * 15 = 75 degrees.

AI explanation

Since the arcs are in the ratio 5:3, the angles they subtend at the center are also in the ratio 5:3. Let the larger angle be $5x$ and the smaller angle be $3x$. We are given the smaller angle as $45^\circ$, so $3x = 45$, which means $x = 15$. The larger angle is $5x = 5 \times 15 = 75^\circ$.

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