CLASSIFYING ANGLES WORKSHEET

Worksheet given in this section will be much useful for the students who would like to practice problems on classifying angles. 

Before look at the worksheet, if you would like to learn how to classify angles, 

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Classifying Angles Worksheet 1 

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°

Classifying Angles Worksheet 2

Problem 1 : 

Find the value of x in the figure given below. 

Problem 2 : 

Find the value of x in the figure given below. 

Problem 3 : 

Find the value of x in the figure given below. 

Problem 4 : 

Find the value of x in the figure given below. 

Problem 5 : 

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

Problem 6 : 

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

Problem 7 : 

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

Problem 8 :

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

Problem 9 : 

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

Problem 10 :

If 2 times the difference between 9 times of angle and 15 is 6450,  find the type of the angle. 

Types of Angles Worksheet 1 - Answers

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

Types of Angles Worksheet 2 - Solutions

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.  

Then,

x° + 2x°  =  90°

Simplify. 

3x  =  90

Divide each side by 3.

x  =  30

So, 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.  

Then,

(x + 1)° + (x - 1)° + (x + 3)°  =  90°

x + 1 + x - 1 + x + 3  =  90

Simplify.

3x + 3  =  90

Subtract 3 from each side. 

3x  =  87

Divide each side by 3.

x  =  29

So, 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. 

Then,

(2x + 3)° + (x - 6)°  =  180°

2x + 3 + x - 6  =  180

Simplify. 

3x - 3  =  180

Add 3 to each side. 

3x  =  183

Divide each side by 3. 

x  =  61

So, 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. 

Then, 

(5x + 4)° + (x - 2)° + (3x + 7)°  =  180°

5x + 4 + x -2 + 3x + 7  =  180

Simplify. 

9x + 9  =  180

Subtract 9 from each side.

9x  =  171

Divide each side by 9.

x  =  19

So, 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. 

Given : 4 times the sum of the angle and 5 is 32.

Then,

4(x + 5)  =  32

Divide each side by 4.

x + 5  =  8

Subtract 3 from each side. 

x  =  3

Because 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. 

Given : 2 times the sum of 3 times of the angle and 20 is 1024.

Then, 

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

Because 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. 

Given : The sum of 5 times of the angle and 2 is 1222.

Then, 

5x + 2  =  1222

Subtract 2 from each side. 

5x  =  1220

Divide each side by 5.

x  =  244

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

Problem 8 : 

If 5 times 2 less than an angle is 440, find the type of the angle. 

Solution :

Let x be the required angle. 

Given : 5 times 2 less than an angle is 440.

Then,

5(x - 2)  =  440

Divide each side by 5. 

x - 2  =  88

Add 2 to each side. 

x  =  90

Angle  =  90°

Because, 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. 

Given : 7 times the difference between 3 times of an angle and 5 is 3745.

Then, 

7(3x - 5)  =  3745

Divide each side by 7. 

3x - 5  =  535

Add 5 to each side. 

3x  =  540

Divide each side by 3.

x  =  180

Because 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. 

Given : 2 times the difference between 9 times of angle and 15 is 6450

2(9x - 15)  =  6450

Divide each side by 2.

9x - 15  =  3225

Add 15 to each side. 

9x   =  3240

Divide each side by 9.  

x  =  360

Because 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 how to classify angles. 

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