Question

If the sum of two adjacent angles is ${100^\circ }$ and one of them is ${35^\circ }$, then the other is
A) ${70^\circ }$
B) $65^\circ $
C) ${135^\circ }$
D) ${145^\circ }$

Answer 1

Hint: In this problem, we have given the sum of two adjacent angles and from those two angles one angle is given. Now our aim is to find the other angle. Let us calculate the required solution.

Complete step-by-step solution:
Sum of the two adjacent angles is equal to ${100^\circ }$.
One of the given angles is ${35^\circ }$.
Let us take the other angle be $x$.
$ \Rightarrow x + {35^\circ } = {100^\circ }$
Keep the variable in one side,
$ \Rightarrow x = {100^\circ } - {35^\circ }$
$ \Rightarrow x = {65^\circ }$
Hence, the other angle is ${65^ \circ }$

$\therefore $ The answer is option (B).

Note: We have to remember that adjacent angles are two angles that have a common vertex and a common side but do not overlap. The angles in the figure which we drew above are also adjacent angles. They share the same vertex and the same common side and no common interior points. Vertical angles are always congruent, which means that they are equal adjacent angles are angles that come out of the same vertex. Two angles are said to be complementary when the sum of the angles is ${90^\circ }$. Any two angles that add up to ${180^\circ }$ degrees are known as supplementary angles.
Two angles having the same vertex and having a common side between them is an adjacent angle. In the solution we have given a diagram in which the given angle and the unknown angles share their sides with each other.