Question

Can two obtuse angles be supplementary?

Answer 1

Hint: Two Angles are Supplementary when they add up to 180 degrees. An obtuse angle is greater than 90 degrees. So, take two obtuse angles and add them to find out whether they are supplementary or not.

Complete step-by-step answer:

We know, two angles are Supplementary when they add up to 180 degrees.
Let us consider the least obtuse angle, i.e., $ > {90^ \circ }$. So, let us take ${91^ \circ }$ and add it to itself. We get-
${91^ \circ } + {91^ \circ } = {182^ \circ }$
We get ${182^ \circ }$, which is greater than ${180^ \circ }$.
Refer the figure of the obtuse angle which is 91 degrees-

Now adding up 91 degrees with itself gives 182 degrees, which is not equal to 180, so figure of supplementary angles is shown below-

Hence, two obtuse angles i.e., angle which is greater than 90 degrees, can never be supplementary as their sum is not coming equal to ${180^ \circ }$ and to be supplementary the angles sum should be equal to ${180^ \circ }$.
If we consider other examples, taking two obtuse angles, ${95^ \circ }$and ${96^ \circ }$.
Adding them we get-
${95^ \circ } + {96^ \circ } = {191^ \circ } > {180^ \circ }$, not supplementary.
So, two obtuse angles can never be supplementary.

Note: Whenever such type of questions appear, take the least value of the type of angle, here in the question obtuse angle is given, so least value of an obtuse angle is ${91^ \circ }$, adding up ${91^ \circ }$ to itself to check whether supplementary or not. Since, we have checked for the least value, if it adds up to ${180^ \circ }$ then obtuse angles sum can be supplementary and if not then cannot be supplementary.