What are Complementary Angles?
Two angles are said to be complementary angles, if the sum of the two angles measure 90 degrees. Thus we can say that two complementary angles together from a right angle measuring 90 degrees. But these two angles need not necessarily be adjacent angles i.e. next to each other.
Example of Complementary Angles
One of the best examples of complementary angles can be seen in right angled triangle. In a right angled triangle, one angle is the right angle. It is a fact that the sum of all the three angles in a right angle is equal to 180 degrees. Thus, it is clear that the sum of the other two non-right angles will be equal to 90 degrees. This means that the two non-right angles in a right angled triangle are complementary angles. In other words, we can say that these two angles complement each other.
Some of the other examples of complementary angles are:
55 degrees, 35 degrees
40 degrees, 50 degrees
67 degrees, 23 degrees
How to Solve Complementary Angles?
Now let us see how to find complementary angles. As we know the definition, finding complementary angles is very easy by applying the definition. If the value of one angle is given, then another angle complementary to that angle is found out by subtracting the given value from 90 degrees.
Consider two angles which are complementary to each other. If one of the angles is 48 degrees, find the other angle.
Solution: If x is the unknown angle, then 48 added to x will give 90 degrees. Therefore, x is given by subtracting 48 from 90. i.e., X = 90-48 = 42 degrees.
Therefore, the other angle is 42 degrees.
Some Complementary Angles Problems will be in the form of slightly confusing word problems.
If one of the complementary angles is six more than twice the other angle, find the angles.
Solution: If the variable Y is considered as one angle measure, then, as per the given statement, the other angle is given by 2Y+6. We know that the sum of the two complementary angles is 90 degrees. So,
Y+2y+6 = 90
3y = 90-6
Therefore the value of Y will be obtained if 84 are divided by 3. Thus, the value of Y will be 28. If y = 28, then the second angle will be (2*28) + 6 which results in the value 62. Thus, the measures of the angle are 28 and 62.