# CENTRAL ANGLES WORKSHEET

Central angles worksheet :

Here we are going to see some practice questions on central angles.

 Question 1 :What is  ∠PSQ? Question 2 :What is  ∠UVT? Question 3 :What is  ∠UWT? Question 4 :What is  ∠AOE and ∠EOD? Question 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°.

Question 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°.

Question 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°.

Question 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°. After having gone through the stuff given above, we hope that the students would have understood "Central angles worksheet".