DETERMINING ANGLE VISUALLY

In geometry, angles can be classified according to the size. There are five different types of angles. 

Type of Angle

Description

Determining angle visually

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°

Practice Problems

Problem 1 :

Find the value of x in the figure given below. 

Solution :

In the above diagram, x° and (2x)° together form a right angle.  

x° + (2x)° = 90°

x + 2x = 90

3x = 90

Divide each side by 3. 

x = 30°

Problem 2 :

Find the value of x in the figure given below. 

Solution :

In the diagram above, (x + 1), (x - 1) and (x + 3) together form a right angle.  

(x + 1) + (x - 1) + (x + 3) = 90°

x + 1 + x - 1 + x + 3 = 90

3x + 3 = 90

Subtract 3 from each side. 

3x = 87

Divide each side by 3.

x = 29

Problem 3 :

Find the value of x in the figure given below. 

In the diagram above, (2x + 3)° and (x - 6)° together form a straight angle.  

(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

Problem 4 :

Find the value of x in the figure given below. 

Solution :

In the diagram above, (5x + 4)°, (x - 2)° and (3x + 7)° together form a straight angle. 

(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

Problem 5 :

Find the value of x in the figure given below. 

In the diagram above, (2x + 4)° is an acute angle. 

0° < (2x + 4)° < 90°

0 < 2x + 4 < 90

Subtract 4 from each value.  

-4 < 2x < 86

Divide each value by 2.

-2 < x < 43

Problem 6 :

Find the value of x in the figure given below. 

In the diagram above, (3x + 9)° is an obtuse angle. 

90° < (3x + 9)° < 180°

90 < 3x + 9 < 180

Subtract 9 from each value.  

81 < 3x < 171

Divide each value by 3.

27 < x < 57

Problem 7 :

Find the value of x in the figure given below. 

In the diagram above, (5x - 5)° is a reflex angle. 

180° < (5x - 5)° < 270°

180 < 5x - 5 < 270

Add 5 to each value.  

185 < 5x < 275

Divide each value by 5.

37 < x < 55

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