Question

Jesper first colored $\frac{1}{2}$ of a circular area, and then he colored $\frac{1}{4}$ of the circular area. What is the angle in degrees that these two parts cover together?

• A. ${150}^o$
• B. ${240}^o$
• C. ${220}^o$
• D. ${270}^o$

Answer 1

The correct option is D ${270}^o$

Jesper first colored $\frac{1}{2}$ of a circular area.

● Write $\frac{1}{2}$ as an equivalent fraction with 360 as the denominator.

$\frac{1}{2}=\frac{1\times 180}{2\times 180}=\frac{180}{360}$

● Write $\frac{180}{360}$ parts of the circle in degrees.

$\frac{180}{360}$ parts of a circle $(={180}^o$

● So, Jesper first colored ${180}^o$of the circular area.

● Next, Jesper colored of the circular area.

● Write $\frac{1}{4}$ as an equivalent fraction with $360$ as the denominator.

$\frac{1}{4}=\frac{1\times 90}{4\times 90}=\frac{90}{360}$

● Write $\frac{90}{360}$ parts of the circle in degrees.

$\frac{90}{360}$ parts of a circle $={90}^o$

● So, Jesper colored $90°$ of the circular area.

● The angle in degrees that these two parts cover together $=180°+90°=270°$

Hence, $B$ is the correct option.