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°
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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