Two angles are supplementary, if they add up to 180⁰.
Example :
120° and 60° are supplementary angles.
Because,
120° + 60° = 180°
Clearly, 120° is the supplement of 60° and 60° is the supplement of 120°.
Problem 1 :
The measure of an angle is 108°. What is the measure of a supplementary angle?
Solution :
Let x be the measure of the required supplementary angle.
Because x and 108° are supplementary angles,
x + 108° = 180°
Subtract 108° from each side.
x = 72°
So, the measure of the supplementary angle is 72°.
Problem 2 :
The measure of an angle is 89°. What is the measure of a supplementary angle?
Solution :
Let x be the measure of the required supplementary angle.
Because x and 41° are supplementary angles,
x + 89° = 180°
Subtract 89° from each side.
x = 91°
So, the measure of the supplementary angle is 91°.
Problem 3 :
Find the value of x :
Solution :
In the diagram shown above, the angles
(2x + 3)° and (x - 6)°
are supplementary angles.
(2x +3)° + (x - 6)° = 180°
2x + 3 + x - 6 = 180
3x - 3 = 180
Add 3 to both sides.
3x = 183
Divide both sides by 3.
x = 61
Problem 4 :
Find the value of x :
Solution :
In the diagram shown above, the angles
(5x + 4)°, (x – 2)° and (3x + 7)°
are supplementary angles.
(5x + 4)° + (x – 2)° + (3x + 7)° = 180°
5x + 4 + x – 2 + 3x + 7 = 180
9x + 9 = 180
Subtract 9 from both sides.
9x = 171
Divide both sides by 9.
x = 19
Problem 5 :
Two angles are supplementary. If one angle is double the other angle, find the two angles.
Solution :
Let x be one of the angles.
Then the other angle is 2x.
Because x and 2x are supplementary angles,
x + 2x = 180°
3x = 180°
Divide both sides by 3.
x = 60°
2x = 2(60°) = 120°
So, the two angles are 60° and 120°.
Problem 6 :
Two angles are supplementary. If one angle is two times the sum of other angle and 3, find the two angles.
Solution :
Let x and y be the two angles which are supplementary.
x + y = 180° ----(1)
Given : One angle is two times the sum of other angle and 3.
x = 2(y + 3)
x = 2y + 6 ----(2)
Now, substitute (2y + 6) for x in (1).
2y + 6 + y = 180
3y + 6 = 180
Subtract 6 from both sides.
3y = 174
Divide both sides by 3.
y = 58
Substitute 58 for y in (2).
x = 2(58) + 6
x = 116 + 6
x = 122
So, the two angles are 122° and 58°.
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