Question

Complementary and supplementary angles need not be
A) measure ${180^ \circ },{90^ \circ }$
B) adjacent
C) angles
D) none

Answer 1

Hint: First recall the concepts of each and every term that is mentioned in the example. Then go through the basic definitions of the angles and the above-mentioned angles. The question asks for what it cannot be so we will eliminate options one by one,

Complete step-by-step answer:
First of all, we will start with the basic definitions of the given angles.
After this whatever is not applicable, we will eliminate the options.
We will start with the complementary angles.
Two angles $\angle A$ and $\angle B$ are said to be complementary angles if $\angle A + \angle B = {90^ \circ }$ .
That means the sum of these measures is the same as the right angle.
Now we will define the supplementary angles.
Two angles $\angle A$ and $\angle B$ are said to be complementary angles if $\angle A + \angle B = {180^ \circ }$ .
That means the sum of these measures is the same as the linear pair.
In the options if you observe carefully, then all the terms are well known other than the term adjacent angles.
So, we will define the adjacent angles.
We call two adjacent angles if they share a common ray.
Now, for the problem, by the definition of the angles, it is clear that option A is always true.
Clearly, option C is always going to be true as well.
Thus, the only thing is that the angles need not be always adjacent.

So, the correct answer is “Option B”.

Note:This is a problem based on the general definition It is a theoretical problem and we don’t have to do any calculation to conclude the final answer. We don’t even have to take any general or special case. Just from the basic definitions, everything is crystal clear.