Question

Identify whether the given pair of angles are either complementary angles or supplementary angles:
\[{10^ \circ },{80^ \circ }\]

Answer 1

Hint- Complementary angle: Two angles are said to be complement to each other if their sum is\[{90^ \circ }\]. I.e. if $a^\circ + b^\circ = 90^\circ $ then the angles a and b are known as complementary angles.
Supplementary angle: Two angles are said to be supplement to each other if their sum is \[{180^ \circ }.\]i.e. $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 angles given\[{10^ \circ },{80^ \circ }\]. 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 angles and if the sum is\[{180^ \circ }\], then the given angles are supplementary angles.
It is given that the two angles are\[{10^ \circ },{80^ \circ }\].
First, we have to find the sum of the given angles.
Here, the sum of the given two angles is \[{10^ \circ } + {80^ \circ } = 90^\circ \]
The sum of given angles is\[{90^ \circ }\].
Hence by the definition of the complementary angles we can come to a conclusion that the two given angles are complementary angles.
Hence, we have identified that the given pair of angles are complementary angles as their sum is\[{90^ \circ }\].

Note: If two angles are supplementary angles and they are said to have one common side and a common vertex, they will also be called adjacent angles. Moreover, the other two sides of these angles will form a straight line.