Question

If there are 24 divisions on a circle, what is the measure of angle for two divisions?

• A. ${15}^{\circ }$
• B. ${20}^{\circ }$
• C. ${25}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

$\text{To determine the measure of the angle}$ $\text{for each division of the circle, we have}$ $\text{to calculate the measure of angle for}$ $\text{one part of the circle.}$

$\text{Fraction of one part of the circle =}$ $\frac{1}{24}$

$\text{Measure of the angle in one complete}$ $\text{circle =}{360}^{\circ }$

$\text{We have to convert}\frac{1}{24}\text{part of the}$ $\text{circle into degrees.}$

$\text{Let's multiply the fraction}\frac{1}{24}\text{by}$ $\text{15 to make an equivalent fraction}$ $\text{with the denominator as 360.}$

$⟹$ $\frac{1\times 15}{24\times 15}=$ $\frac{15}{360}$

$\text{Hence, each part of a circle measures}$ $\text{as}{15}^{\circ }\text{.}$

$\text{Two parts of the circle will measure}$
$⟹2\times {15}^{\circ }={30}^{\circ }$

$\text{Hence, the total angle between 2}$ $\text{divisions of circle is}{30}^{\circ }\text{.}$