Question

Identify whether the given pair of angles are either complementary angles or supplementary angles:
\[{100^ \circ },{80^ \circ }\]

Answer 1

Hint: Complementary angle: Two angles are said to be a complement to each other if their sum is\[{90^ \circ }\]. That is if $a^\circ + b^\circ = 90^\circ $ then we call the angles a and b as complementary angles.
Supplementary angle: Similarly, when the sum of two angles is equal to \[{180^ \circ }.\] We call them supplementary angles. That is when $a^\circ + b^\circ = 180^\circ $ then the angles a and b are known as supplementary angles.

Complete step by step answer:
Let us consider the two given angles are \[{100^ \circ },{80^ \circ }\]. To find whether they are complementary or supplementary angles we know we have to find the sum of these two given angles.
If the sum is \[{90^ \circ }\], then the given angles are complementary and if the sum is \[{180^ \circ }\], then the given angles are supplementary.
Let us calculate the sum of the angles.

Here, the sum of the given two angles is \[{100^ \circ } + {80^ \circ } = {180^ \circ }\]The sum of the given angles is \[{180^ \circ }\].
Hence by the definition of the supplementary angles, we can conclude that the two angles are supplementary.
Hence, we have identified that the given pair of angles are supplementary angles as their sum is \[{180^ \circ }\].
Additional information: If two angles are supplementary and they have one common side and a common vertex, we can call them adjacent angles. In the above given diagram \[{100^ \circ },{80^ \circ }\] are adjacent angles and A is the adjacent vertex. Moreover, the other two sides of these angles will form a straight line.

Note:
To solve these type questions easily, we have to remember that the addition of the given angles is either $a^\circ + b^\circ = 90^\circ $or $a^\circ + b^\circ = 180^\circ $. From the result of the addition, we call the angle is the complementary angle or supplementary angle.