Question

Can two adjacent angles be supplementary? Draw figure.

Answer 1

Hint: We will look over basic definitions of adjacent angle and supplementary angle to answer this question. Basically, when two angles have a common side and a common vertex(corner point) and if they overlap then this pair of angles are called adjacent angles.

Complete step-by-step solution -
Here angle 1 is adjacent to angle 2, whereas when the sum of angle 1 and angle 2 is 90 degree, these angles are called supplementary angles.

It is given in the question that we have to find out that are the two adjacent angles supplementary. Before deciding, we have to look at the basic definition of the adjacent angles, supplementary angles and complementary angles.
When two angles have a common side and a common vertex (Corner point) and if they don’t overlap each other they are said to be adjacent angles.

Here in the above figure we have $\mathrm{\angle }AOC\text{and}\mathrm{\angle }COB$ in which they both have side OC as common also vertex O is common in both. From the figure it is clear that $\mathrm{\angle }AOC\text{and}\mathrm{\angle }COB$ don’t overlap each other, which means that $\mathrm{\angle }AOC\text{and}\mathrm{\angle }COB$ are adjacent angles.

Complementary angles are the pair of adjacent angles in which the sum of two angles is equal to 90 degree.

$\mathrm{\angle }COB+\mathrm{\angle }BOA=90$, thus they are complementary angles.
Supplementary angles are the pairs of adjacent angles in which the sum of two angles is equal to 180 degree.

$\mathrm{\angle }AOB+\mathrm{\angle }BOC=180{}^{\circ }$ These two angles are forming linear pairs and we know that linear pairs are equal to 180, thus forming supplementary angles.
Now, in question consider the following situation of pair of angles, $\mathrm{\angle }AOB=90{}^{\circ }$ and $\mathrm{\angle }BOC=90{}^{\circ }$ as well.

Also These angles are adjacent, according to the definition of adjacent angles, and these pairs of angles sum to 180 degree such that $\mathrm{\angle }AOB+\mathrm{\angle }BOC=90+90=180{}^{\circ }$, forming a supplementary pair of angles. Therefore, It is possible that two adjacent angles form supplementary angles.

Note: This is a very basic question on angles. Students may confuse between complementary angle and supplementary angle but if we know the basic definition of supplementary angles and complementary angles and the difference between them, then it will be very easy to solve such problems.