# CLASSIFYING ANGLES

In geometry, angles can be classified according to the size.

There are six different types of angles.

Type of Angle

Description

Example

Acute angle

An angle less than 90°

Right angle

An angle exactly 90°

Obtuse angle

An angle greater than 90° but less than 180°

Straight angle

An angle exactly 180°

Reflex angle

An angle greater than 180° but less than 360°

Full angle

An angle exactly 360°

Classify the angles as acute, right, obtuse straight, reflex or full angle  :

1)   25°  ---> Acute angle

2)   75°  ---> Acute angle

3)   98°  ---> Obtuse angle

4)   145°  ---> Obtuse angle

5)   215°  ---> Reflex angle

6)   180°  ---> Straight angle

7)   90°  ---> Right angle

8)   360°  ---> Full angle

9)   18°  ---> Acute angle

10)   270°  ---> Reflex angle

## Solved Problems

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.

According to the question, we have

4(x + 5)  =  32

Divide each side by 4.

x + 5  =  8

Subtract 5 from each side.

x  =  3

Angle  =  3°

Because the angle 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 :

Let x be the required angle.

According to the question, we have

2(3x + 20)  =  1024

Divide each side by 2.

3x + 20  =  512

Subtract 20 from each side.

3x  =  498

Divide each side by 3.

x  =  166

Angle  =  166°

Because the angle 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 :

Let x be the required angle.

According to the question, we have

5x + 2  =  1222

Subtract each side by 2.

5x  =  1220

Divide each side by 5.

x  =  244

Angle  =  244°

Because the angle 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 :

Let x be the required angle.

According to the question, we have

5(x - 2)  =  440

Divide each side by 5.

x - 2  =  88

x  =  90

Angle  =  90°

Because 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 :

Let x be the required angle.

According to the question, we have

7(3x - 5)  =  3745

Divide each side by 7.

3x - 5  =  535

3x  =  540

Divide each side by 3.

x  =  180

Angle  =  180°

Because the angle is exactly 180°, the type of the angle is straight angle

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