Two angles are complementary, if they add up to 90⁰.
Example :
30° and 60° are complementary angles.
Because,
30° + 60° = 90°
Clearly, 30° is the complement of 60° and 60° is the complement of 30°.
Problem 1 :
The measure of an angle is 41°. What is the measure of a complementary angle?
Solution :
Let x be the measure of the required complementary angle.
Because x and 41° are complementary angles,
x + 41° = 90°
Subtract 41° from each side.
x = 49°
So, the measure of the complementary angle is 49°.
Problem 2 :
The measure of an angle is 62°. What is the measure of a complementary angle?
Solution :
Let x be the measure of the required complementary angle.
Because x and 62° are complementary angles,
x + 62° = 90°
Subtract 62° from each side.
x = 28°
So, the measure of the complementary angle is 28°.
Problem 3 :
Find the value of x :
Solution :
From the picture above, it is clear that the angles x and 2x are complementary.
x + 2x = 90°
3x = 90
Divide each side by 3.
x = 30
So, the value of x is 30.
Problem 4 :
Find the value of x :
Solution :
In the picture above, the angles
(x + 1)°, (x - 1)° and (x + 3)°
are complementary.
(x + 1)° + (x - 1)° + (x + 3)° = 90°
(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
So, the value of x is 29.
Problem 5 :
Two angles are complementary. If one of the angles 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 complementary angles, we have
x + 2x = 90°
3x = 90
Divide each side by 3.
x = 30
And,
2x = 2(30) = 60
So, the two angles are 30° and 60°.
Problem 6 :
Two angles are complementary. 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 complementary.
x + y = 90° ----(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 = 90
3y + 6 = 90
Subtract 6 from each side.
3y = 84
Divide each side by 3.
y = 28
Substitute 28 for y in (2).
x = 2(28) + 6
x = 56 + 6
x = 62
So, the two angles are 62° and 28°.
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