**Central angle of a circle : **

Central angles are angles formed by any two radii in a circle. The vertex is the center of the circle

The central angle of circle is 360°.

**Example 1 :**

What is ∠PSQ?

**Solution :**

**Since the central angles of a circle is 360 degree,**

**∠PSQ + **∠QSR + ∠RSP = 360°

**∠PSQ + 80**° + 140° = 360°

**∠PSQ + 120**° = 360°

**∠PSQ ** = 360° - ** 120**°

**∠PSQ ** = 240°

Hence the required angle is 240°.

**Example 2 :**

What is ∠UVT?

**Solution :**

**Since the central angles of a circle is 360 degree,**

**∠SVU + **∠UVT + ∠TVS = 360°

**140**°** + **∠UVT + 130° = 360°

**270**°** + **∠UVT = 360°

∠UVT = 360° - 270°

∠UVT = 90°

Hence the required angle is 90°.

**Example 3 :**

What is ∠UWT?

**Solution :**

**Since the central angle of a circle is 360 degree,**

**∠VWU + **∠UWT + ∠TWV = 360°

**130**°** + **∠UWT + 80° = 360°

**210**°** + **∠UWT = 360°

∠UWT = 360° - 210°

∠UWT = 150°

Hence the required angle is 150°.

**Example 4 :**

What is ∠AOE and ∠EOD?

**Solution :**

**Since AD is a straight line, the measure of angle AOD is 180 degree**

**∠AOE + EOD **= 180°

**x + 138**°** + x **+ 48° = 180°

2x + 186° = 180°

By subtracting 186° on both sides, we get

2x + 186° - 186° = 180° - 186°

2x = 180° - 186°

2x = -6

Divide by 2 on both sides, we get

x = -3

∠AOE = -3 + 138 = 135°

∠EOD = -3 + 48 = 45°

Hence the required angles are 135° and 45°.

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