**Types of Angles Worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on types of angles.

Before look at the worksheet, if you know the different types of angles,

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

1) 35°

2) 85°

3) 95°

4) 135°

5) 205°

6) 180°

7) 90°

8) 360°

9) 15°

10) 270°

1) Find the value of "x" in the figure given below.

2) Find the value of "x" in the figure given below.

3) Find the value of "x" in the figure given below.

4) Find the value of "x" in the figure given below.

5) If 4 times the sum of an angle and 5 is 32, find the type of the angle.

6) If 2 times the sum of 3 times of an angle and 20 is 1024, find the type of the angle.

7) If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.

8) If the sum of 5 times of an angle and 2 is 1222, find the type of the angle.

9) If 7 times the difference between 3 times of an angle and 5 is 3745, find the type of the angle.

10) If 2 times the difference between 9 times of angle and 15 is 6450, find the type of the 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 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles "x" and "2x" together form a right angle.

So, we have x + 2x = 90°

3x = 90°

x = 30°

Hence the value of "x" is 30°.

**Problem 2 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (x+1), (x-1) and (x+3) together form a right angle.

So, we have (x+1) + (x-1) + (x+3) = 90

3x + 3 = 90

3x = 87

x = 29

Hence the value of "x" is 29.

**Problem 3 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (2x+3) and (x-6) together form a straight angle.

So, we have (2x+3) + (x-6) = 180°

2x + 3 + x - 6 = 180°

3x - 3 = 180

3x = 183

x = 61

Hence the value of "x" is 61.

**Problem 4 :**

Find the value of "x" in the figure given below.

**Solution :**

From the picture above, it is very clear that the angles (5x+4), (x-2) and (3x+7) together form a straight angle.

So, we have (5x+4) + (x-2) + (3x+7) = 180°

5x + 4 + x -2 + 3x + 7 = 180°

9x + 9 = 180

9x = 171

x = 19

Hence the value of "x" is 19.

**Problem 5 : **

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°

Since the angle 3° is less than 90°, the type of the angle is acute angle.

**Problem 6 : **

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°

Since the angle 166° is greater than 90° but less than 180°, the type of the angle is obtuse angle.

**Problem 7 : **

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°

Since the angle 244° is greater than 180° but less than 360°, the type of the angle is reflex angle.

**Problem 8 : **

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°

Since the angle is exactly 90°, the type of the angle is right angle.

**Problem 9 : **

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°

Since the angle is exactly 180°, the type of the angle is straight angle.

**Problem 10 : **

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°

Since the angle is exactly 360°, the type of the angle is full angle.

After having gone through the stuff given above, we hope that the students would have understood the different types of angles.

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