Question

If the given statement is true then enter 1 and if false then enter 0
Statement: Can two adjacent angles be supplementary?

Answer 1

Hint: To solve this problem, we should know the basics of adjacent angles and some of the geometric figures where we observe the application of the adjacent figures, and then we can infer the correct answer.

Complete step-by-step answer:
Two angles are said to be supplementary angles if and only if there sum equal to \[{180^0}\].
Yes, two adjacent angles can be supplementary. This can happen in two cases.
Case 1: If both the adjacent angles are right angles as shown in the below figure:

Here, all the adjacent sides in the square and rectangle are right angles \[{90^0}\].
So, the sum of adjacent angles is \[{90^0} + {90^0} = {180^0}\] i.e., supplementary.
Case 2: If one of the angles is acute and the other angle is obtuse as shown in the below figure:

Here, if we have taken one acute angle as \[{70^0}\] and the other obtuse angle as \[{110^0}\] then their sum is \[{70^0} + {110^0} = {180^0}\] i.e., supplementary.
For both cases, we can have the sum of two angles as supplementary.
Hence, the given statement is true and we have to enter 1.

Note: To solve these kinds of questions, we have to identify whether a statement is correct or incorrect based, we try to take a few cases related to the statement given. Then, if we can prove that problem is correct in some cases and incorrect in others, then we can say that the data is insufficient.