# TYPES OF ANGLES

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

There are six different types of angles.

Let us see, how how angles in geometry can be classified.

Type of Angle

Description

Example

Acute angle

An angle that is less than 90° Right angle

An angle that is exactly 90° Obtuse angle

An angle that is greater than 90° but less than 180° Straight angle

An angle that is exactly 180° Reflex angle

An angle that is greater than 180° but less than 360° Full angle

An angle that is exactly 360° 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

## Word 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

4x + 20  =  32

4x  =  12

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

3x + 20  =  512

3x  =  498

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

5x  =  1220

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

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

3x - 5  =  535

3x  =  540

x  =  180

Angle  =  180°

Because 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 :

Let x be the required angle.

According to the question, we have

2(9x - 15)  =  6450

9x - 15  =  3225

9x   =  3240

x  =  360

Angle  =  360°

Because the angle is exactly 360°, the type of the angle is full angle Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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