Supplementary angles explained

Did you learn about supplementary angles? These are some special type of angles that every student should learn. The meaning of supplementary angles is quite simple so it is easy to learn and remember. Where we can make use of these supplementary angles? We have so many applications in that one of the applications is while learning about transversal and parallel lines concept we will make use of this supplementary angles.

The definition of Supplementary angles:

Any two angles are called as supplementary angles if the sum is equals to 180° .

Examples:

25° and 155°

95° and 85°

127° and 53°

The above mentioned all the three pairs are supplementary angles because sum gives 180°.

Important note on supplementary angles:

♠ Can we say that any two acute angles become supplementary? The answer is “NO”. definitely two acute angles sum won’t be 180° because highest acute angle is 89° so eventhough if you take both angles as 89° its sum is equals to 178° only.

♠ In similar way can two right angles become supplementary? Here the answer is “YES”. No doubt in that.

♠ What about two obtuse angles? Can they become supplementary angles? For this the answer is “NO”. because if we take the least obtuse angle also i.e. 91°, if both the angles are 91° then the sum of that two obtuse angles are equals to 182°.

Examples:

♦ If the two angles are supplementary and one of them is 67° then find the other angle.

Solution:

Given

One angle = 67°

As two angles are supplementary so 67° + y = 180°. Therefore y = 113°.

♦ The supplementary angles are in the ratio 7: 2, and then find the angles.

Solution:

Given

The two angles are in the ratio 7: 2

Let the two angles be 7x° and 2x°

According to problem,

7x° + 2x° = 180°

9x° = 180°

x = 20

Therefore the two angles are 7x° = 7 x 20° = 140° and 2x° = 2 x 20° = 40° 