Question

The circle is divided into 15 equal parts. What is the measure of the angle for the blue region?

• A. ${100}^{\circ }$
• B. ${130}^{\circ }$
• C. ${110}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is D ${120}^{\circ }$

$\text{The circle is basically divided into 3}$ $\text{colored sections, blue, red and green.}$

$\text{Each colored section is further divided}$ $\text{into 5 equal parts.}$

$\text{We need to calculate the total angle}$ $\text{of the blue region.}$

$\text{Blue region covers}\frac{1}{3}\text{part of the}$ $\text{circle.}$

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

$\text{We have to convert}\frac{1}{3}\text{part of the}$ $\text{circle into degrees.}$

$\text{Let's multiply the fraction}\frac{1}{3}\text{by}$ $\text{120 to make an equivalent fraction}$ $\text{with the denominator as 360.}$

$⟹$ $\frac{1\times 120}{3\times 120}=$ $\frac{120}{360}$

$\text{So,}\frac{1}{3}\text{part of a circle measures}$ $\text{as}{120}^{\circ }\text{.}$

$\text{Hence, the total angle in the blue}$ $\text{region is}{120}^{\circ }\text{.}$