Question

A monster cuts $\frac{1}{4}$ part of a circular stone and then again cuts $\frac{1}{6}$ part from the same stone. What is the angle in degrees that these two parts cover together?

• A. ${170}^o$
• B. ${150}^o$
• C. ${120}^o$
• D. ${140}^o$

Answer 1

The correct option is B ${150}^o$

The monster firstly cut $\frac{1}{4}$ of a circular stone.

● 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 the monster first cut ${90}^o$ of the circular stone.

● Next, the monster cut $\frac{1}{6}$ of a circular stone.

● 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, the monster cut 60° of the circular stone.

● The angle in degrees that these two parts cover together $=90°+60°=150°$

Hence, $A$ is the correct option.