Question

Raju says “supplementary angle of \[115^\circ \] is \[65^\circ \]”. Do you agree with Raju? Give reason.

Answer 1

Hint:
Here we need to check whether the given statement is true or not. We will use the concept of supplementary angles to check the statement said by Raju. We will find the sum of these two angles and if we will get the same value according to the definition of the supplementary angles then the given statement will be true.

Complete step by step solution:
It is given that the supplementary angle of \[115^\circ \] is \[65^\circ \].
We will first define the term supplementary angles. Supplementary angles are defined as a pair of angles whose sum is equal to \[180^\circ \].
So, we will first find the sum of these two given angles.
Sum of angles \[ = 115^\circ + 65^\circ = 180^\circ \]
Here we can see that the sum of these two angles is equal to \[180^\circ \].
Therefore, these two angles are supplementary angles i.e. supplementary angle of \[115^\circ \] is \[65^\circ \].

So yes, we agree with Raju’s statement that the supplementary angle of \[115^\circ \] is \[65^\circ \].

Note:
The supplementary angles together makes a straight line. If two angles are supplementary then one will obtuse angle and the other will be acute angle or both will be right angle. Here, we can get confused and instead of adding the two angles, we might subtract it, which will not give us the required answer. Also we might get confused between complementary and supplementary and answer that the angles is not supplementary, which is again an incorrect answer. If we get the sum of two angles as \[90^\circ \] then they are said to be complementary angles.