Question

$\frac{1}{2}$ of the dartboard is colored blue and $\frac{1}{6}$ of it is colored green. What is the angle in degrees that these two parts cover together?

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

Answer 1

The correct option is D ${240}^o$

$\frac{1}{2}$ of the dartboard is colored blue.

● 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 $180°$ of the dartboard is colored blue.

● Next, $\frac{1}{6}$ of it is colored green.

● Write $\frac{1}{6}$ as an equivalent fraction with $360$ as the denominator.

$\frac{1}{6}=\frac{1\times 60}{6\times 60}=\frac{60}{360}$

● Write $\frac{60}{360}$ parts of the circle in degrees.

$\frac{60}{360}$ parts of a circle $={60}^o$

● So $60°$ of the dartboard is colored green.

● Two parts together cover $=180°+60°=240°$

Hence, $D$ is the correct option.