Question

A circle is divided into 9 equal parts.
What is the measure of the angle for each division of the circle?

• A. ${40}^{\circ }$
• B. ${45}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A ${40}^{\circ }$

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

$\text{Fraction of one part of the circle =}$ $\frac{1}{9}$

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

$\text{We have to convert}\frac{1}{9}\text{part of the}$ $\text{circle into degrees.}$

$\text{Let's multiply the fraction}\frac{1}{9}\text{by}$ $\text{40 to make an equivalent fraction}$ $\text{with the denominator as 360.}$

$⟹$ $\frac{1\times 40}{9\times 40}=$ $\frac{40}{360}$

$\text{Hence, each part of a circle measures}$ $\text{as}{40}^{\circ }\text{.}$