In geometry, angles can be classified according to the size. There are six different types of angles.
An angle that is greater than 0° and less than 90° is called acute angle.
Example :
An angle that is exactly 90° is called right angle.
Example :
An angle that is greater than 90° and less than 180° is called obtuse angle.
Example :
An angle that is exactly 180° is called right angle.
Example :
An angle that is greater than 180° and less than 360° is called reflex angle.
Example :
An angle that is exactly 360° is called full angle.
Example :
Classifying angles as acute, right, obtuse straight, reflex or full angle :
1) 35° ----> Acute angle
2) 85° ----> Acute angle
3) 95° ----> Obtuse angle
4) 135° ----> Obtuse angle
5) 205° ----> Reflex angle
6) 180° ----> Straight angle
7) 90° ----> Right angle
8) 360° ----> Full angle
9) 15° ----> Acute angle
10) 270° ----> Reflex angle
Problem 1 :
If 4 times the sum of an angle and 5 is 32, find the type of the angle.
Solution :
Let x be the required angle.
4(x + 5) = 32
4x + 20 = 32
4x = 12
x = 3
Angle = 3°
Since 3° is less than 90°, the type of the angle is acute angle.
Problem 2 :
If 2 times the sum of 3 times of an angle and 20 is 1024, find the type of the angle.
Solution :
2(3x + 20) = 1024
3x + 20 = 512
3x = 498
x = 166
Angle = 166°
Since 166° is greater than 90° but less than 180°, the type of the angle is obtuse angle.
Problem 3 :
If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.
Solution :
5x + 2 = 1222
5x = 1220
x = 244
Angle = 244°
Since 244° is greater than 180° but less than 360°, the type of the angle is reflex angle.
Problem 4 :
If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.
Solution :
5(x - 2) = 440
x - 2 = 88
x = 90
Angle = 90°
Since the angle is exactly 90°, the type of the angle is right angle.
Problem 5 :
If 7 times the difference between 3 times of an angle and 5 is 3745, find the type of the angle.
Solution :
7(3x - 5) = 3745
3x - 5 = 535
3x = 540
x = 180
Angle = 180°
Since the angle is exactly 180°, the type of the angle is straight angle.
Problem 6 :
If 2 times the difference between 9 times of angle and 15 is 6450, find the type of the angle.
Solution :
2(9x - 15) = 6450
9x - 15 = 3225
9x = 3240
x = 360
Angle = 360°
Since the angle is exactly 360°, the type of the angle is full angle.
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