Question

Freddie was fencing a circular playground. In his first shift, he fenced $\frac{1}{2}$of the ground, in his second shift he fenced $\frac{1}{5}$ of it, and in his third shift, he fenced $\frac{2}{36}$ of the playground. What angle of the playground did he fence?

• A. ${180}^0$
• B. ${20}^0$
• C. ${72}^0$
• D. ${272}^0$

Answer 1

The correct option is D ${272}^0$

To find the total angle of the playground fenced, we need to find the angle subtended in each shift.
To calculate the angle formed by a fraction of the circle, we need to find an equivalent fraction with the denominator $360$.
In the first shift:
Fraction of playground fenced $=\frac{1}{2}$
Measure of angle that covers $\frac{1}{2}$ the complete round: $\frac{1}{2}=\frac{1}{2}\times \frac{180}{180}=\frac{180}{360}$
$\frac{180}{360}$ parts of the circle in degrees $={180}^0$
In the second shift:
Fraction of playground fenced $=\frac{1}{5}$
Measure of angle that covers $\frac{1}{5}$ of the complete round: $\frac{1}{5}=\frac{1}{5}\times \frac{72}{72}=\frac{72}{360}$
$\frac{72}{360}$ parts of the circle in degrees $={72}^0$

In the third shift:
Fraction of playground fenced: $\frac{2}{36}$
Measure of angle that covers $\frac{2}{36}$ of the complete round: $\frac{2}{36}=\frac{2}{36}\times \frac{10}{10}=\frac{20}{360}$
$\frac{20}{360}$ parts of the circle in degrees $={20}^0$

Total angle of the playground fenced $={180}^0+{72}^0+{20}^0={272}^0$