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°

**Classify the 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.

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.

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