$\frac{5}{6}$ of complete angle equals to ?

Question

Accepted Answer

The correct option is 2:
First, let's recall what a complete angle is. A complete angle is an angle that measures $360^{\circ}$.
The question asks us to find the value of $\frac{5}{6}$ of a complete angle.
To do this, we need to multiply the fraction $\frac{5}{6}$ by the measure of a complete angle, which is $360^{\circ}$.

Step-by-step calculation:
We need to calculate $\frac{5}{6}$ of $360^{\circ}$.
This can be written as:
$ \frac{5}{6} 	imes 360^{\circ} $
Now, we perform the multiplication:
$ \frac{5 	imes 360^{\circ}}{6} $
We can simplify by dividing $360$ by $6$:
$ 360 \div 6 = 60 $
Substitute this back into the expression:
$ 5 	imes 60^{\circ} $
Finally, multiply $5$ by $60$:
$ 5 	imes 60^{\circ} = 300^{\circ} $
So, $\frac{5}{6}$ of a complete angle is $300^{\circ}$. This matches Option 2.

The incorrect option is 1:
$200^{\circ}$ is incorrect. This would be $\frac{200}{360} = \frac{20}{36} = \frac{5}{9}$ of a complete angle, not $\frac{5}{6}$.

The incorrect option is 3:
$360^{\circ}$ is incorrect. $360^{\circ}$ is the measure of the complete angle itself, not $\frac{5}{6}$ of it.

The incorrect option is 4:
$180^{\circ}$ is incorrect. This would be $\frac{180}{360} = \frac{1}{2}$ of a complete angle (a straight angle), not $\frac{5}{6}$.