Question

If two adjacent angles are equal, then each angle measures 90 degrees. Select the correct option –
(a) True
(b) False
(c) Ambiguous
(d) Data insufficient

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:
In a figure, the adjacent angles can be defined as two angles that have a common vertex and a common side. To explain, we see from the figure below, we have angles c and angle d are the adjacent angles (such that the sum of their angles is 90 degrees) since they share a common vertex and a common side.

In case of quadrilaterals, two angles of a quadrilateral having a common arm are called its adjacent angles. In the given figure below, (∠A, ∠B), (∠B, ∠C), (∠C, ∠D) and (∠D, ∠A) are four pairs of adjacent angles of quadrilateral ABCD. (in this case the quadrilateral is a rectangle)

We can see that in the first case, we have that the sum of angles is 90 degrees, so clearly each of the angles is different from 90 degrees. However, in the second case (for rectangle), each adjacent angle was equal to 90 degrees. Thus, we can say that in the given question, we have insufficient data to conclude the final answer.
Hence, the correct answer is (d) Data insufficient.
Note: To solve the question, where 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.