Question

Question 2(ii)
A group of 360 people were asked to vote for their favourite season from the seasons rainy, winter and summer.
Find the central angle of each sector.

Answer 1

Central angle of summer season
= $\frac{{90}^{\circ }\times {360}^{\circ }}{{360}^{\circ }}={90}^{\circ }$

Central angle of rainy season
= $\frac{{120}^{\circ }\times {360}^{\circ }}{{360}^{\circ }}={120}^{\circ }$

Central angle of winter season
= $\frac{{150}^{\circ }\times {360}^{\circ }}{{360}^{\circ }}={150}^{\circ }$.

But if we observe, clearly there is no need for calculation in this question as the value of a complete central angle in a circle is
${360}^{\circ }$, and the total number of people are also $360$ so $1^{\circ }$ = $1$ person.
So, central angles will be the same as the number of people in that group.