Before dealing with the problems let us study how to find the central angle.

**Step 1 :** Read the given problem and list out the given quantities.

**Step 2 :** The Central angle formula is given by

Central angle = $\frac{Arc\ length \times 180^{o}}{\pi \times\ Radius}$

substitute all the values and get the answer.### Solved Examples

**Question 1: **Find the central angle if Arc length is 5m and radius is 2 m.

** Solution: **

Given : Arc length = 5m,

Radius = 2m

The central angle is given by

Central angle = $\frac{Arc\ length \times 180}{\pi \times\ Radius}$

= $\frac{5 m \times 180^{o}}{3.142 \times 2m}$

= 143.312^{o}.

**Question 2: **Find the central angle if Arc length is 2m and radius is 1 m.

** Solution: **

Given : Arc length = 2m,

Radius = 1m

The central angle is given by

Central angle = $\frac{Arc\ length \times 180}{\pi \times\ Radius}$

= $\frac{2m \times 180^{o}}{3.142 \times 1m}$

= 114.65^{o}.