Question

Can two obtuse angles be supplementary$?$

Answer 1

Hint: We can say that two angles are supplementary angles if and only if the addition of two angles are ${180^o}$. In other words, we can say that, if the addition of two angles can make a straight line then those angles are called supplementary angles.

Complete step by step solution:
First, let us learn about the obtuse angle, then we can show whether obtuse angles make supplementary angles or not.
 Obtuse angles are those angles whose measurements are greater than ${90^ \circ }$ but lesser than ${180^ \circ }$. In other words, the angle lies between ${90^ \circ }$ and ${180^ \circ }$.
For example: ${120^ \circ }$ is an obtuse angle.
${135^ \circ }$ lies between ${90^ \circ }$ and ${180^ \circ }$.
Example is shown as in the below figure.

Now, we shall know what supplementary angles are.
Two angles are supplementary when they measure up to ${180^ \circ }$. They should make a straight line when two angles are added to form a supplementary angle.
For example: angles ${75^ \circ }$ and ${105^ \circ }$ upon adding gives ${180^ \circ }$.
Below figure shows an example for supplementary angles.

Now, the question is can two obtuse angles can make supplementary angle or not$?$
From the above discussion, we can clearly say that two obtuse angles cannot form supplementary angles because, obtuse angle will be greater than ${90^ \circ }$ and less than ${180^ \circ }$. If two obtuse angles are added then the result will be greater than ${180^ \circ }$ which is not a supplementary.

Note:
It is not mandatory to have only two angles to form a supplementary angle, we can have more than two angles also. But the condition is the sum of these angles should be ${180^ \circ }$. For example if we have three angles like ${30^ \circ }$, ${90^ \circ }$ and ${60^ \circ }$ then it will form a straight line which is supplementary.