Question

If true then enter 1 and if false enter 0.
Can two obtuse angles be complementary to each other?

Answer 1

Hint: We are given a question based on obtuse angles property. We are asked to tell if two obtuse angles can be complementary to each other or not. First of all obtuse angles are those which have a value greater than \[{{90}^{\circ }}\]. And complementary angles means the angles when added up gives the value \[{{90}^{\circ }}\]. Clearly, both the statements contradict each other as obtuse angles when added up, their sum even exceeds \[{{180}^{\circ }}\]. Hence, we have the answer to the given question.

Complete step-by-step solution:
According to the given question, we are given a question based on the property of angles especially of obtuse angles. We are asked to tell whether two obtuse angles complement each other or not.
Obtuse angle refers to those angles which have a value which is greater than \[{{90}^{\circ }}\] but less than \[{{180}^{\circ }}\], that is, it lies between \[{{90}^{\circ }}\] and \[{{180}^{\circ }}\].
For example - \[{{160}^{\circ }},{{120}^{\circ }},{{110}^{\circ }}\], etc.
And complementary angles refer to those angles which when added up gives the sum as \[{{90}^{\circ }}\].
For example - \[{{60}^{\circ }}and{{30}^{\circ }}\] are complementary angles as their sum is equal to \[{{90}^{\circ }}\].
In the question, we are asked if two obtuse angles complement each other or not.
Both ‘obtuse angles’ and ‘complement’ are terms that contradict each other.
We have stated the earlier that obtuse angles have values greater than \[{{90}^{\circ }}\], then it is unthinkable to have two obtuse angles which will add up to give a sum of \[{{90}^{\circ }}\]. Rather, when two obtuse angles are added up their sum is greater than \[{{180}^{\circ }}\].
Therefore, the answer is 0.

Note: The obtuse angle should not be misunderstood for acute angle or right angle. An acute angle is an angle which has a value less than \[{{90}^{\circ }}\] but greater than \[{{0}^{\circ }}\]and a right angle has a value of \[{{90}^{\circ }}\]. An obtuse angle is an angle which has a value greater than \[{{90}^{\circ }}\] but less than \[{{180}^{\circ }}\]. So, also there is another type of angle as well, which we call, reflex angle. It is an angle which has a value greater than \[{{180}^{\circ }}\] but less than \[{{360}^{\circ }}\]. For example - \[{{270}^{\circ }}\] is a reflex angle.