What are Supplementary Angles?
If you are given the measures of two angles and it’s also stated that their sum is equal to 180°, then, the two angles are said to be supplementary angles.
For instance, in the image we can see that two angles, 40° and 140° add up to 180°. Hence, 40° and 140° form a ‘pair’ of supplementary angles. It is to be noted that in this example 40° and 140° also form a linear pair or a straight angle. Hence, all linear pairs of angles are supplementary angles.
Few other examples of supplementary angles are, 30° and 150°, 100° and 80°, 50° and 130°, and 90° and 90°.
Non Adjacent Supplementary Angles
As mentioned earlier, all linear pairs of angles are supplementary angles, however, not all supplementary angles form linear pairs. This is because two non adjacent angles can also form a pair of supplementary angles. Let’s consider an example:
Here, we have two non-adjacent angles that measure 130° and 50°. These two angles add up to 180°, thus forming a ‘supplementary pair’.
Solved Examples
Example 1: (y – 60)° and (y + 100)° are the measures of two supplementary angles. Find the measure of each angle.
Solution: In order to find the measure of each angle, we will find the value of ‘y’.
We know that the sum of two supplementary angles is 180°.
So,
\(\left ( y – 60 \right )^{ \circ }+\left( y+100 \right)^{\circ }=180^{\circ }\)
\(y-60+y+100=180\) [Rewrite addition equation]
\(2y+40=180\) [Combine like terms]
\(2y=140\) [Subtract 40 from both sides]
\(y=70\) [Divide by 2 on both sides]
Hence, the value of y is 70°.
Now substitute the value of y in the each expression in the problem:
\(\left( y-60 \right)^{\circ } = \left( 70 – 60 \right)^{\circ }\)
\(= 10^{\circ }\) and
\(\left( y + 100 \right)^{\circ } = \left( 70 + 100 \right)^{\circ }\)
\(= 170^{\circ }\)
So, the two angle measures are 10° and 170°.
Example 2: Find the value of x.
Solution:
From the given diagram, we can say that both the angles are supplementary to each other so their sum will give 180°.
So,
\(\left( x-40 \right)^{\circ } – 3x^{\circ } = 180^{\circ }\)
\(4x – 40 = 180 \) [Simplify]
\(4x = 220 \) [Add 40 on both sides]
\(x = 55\) [Divide by 4 on both sides]
Hence, the value of x is 55°.
Example 3: Which of the following pair of angles is not supplementary?
Solution:
We know that the sum of supplementary angles is 180°. Now, we will check whether the pair of angles provided in the problem are supplementary angles.
For the first pair, the angles 123° and 57° add up to give 180°. Hence, this pair of angles are supplementary.
For the second pair, the angles 72° and 118° add up to give 190° so the two angles are not supplementary angles.
Thus, the second pair of angles are not supplementary.
Two angles are said to be complementary if their measures add up to give 90°.
Yes, two right angles are supplementary to each other as their sum results in 180°.
Two obtuse angles cannot be supplementary to each other as the sum of their measures will not be 180°. The sum of two obtuse angles is always greater than 180°.
While complementary angles add up to give 90°, supplementary angles add up to give 180°.