Answer
Verified
492.3k+ views
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 $\angle AOC\ \text{and}\ \angle COB$ in which they both have side OC as common also vertex O is common in both. From the figure it is clear that $\angle AOC\ \text{and}\ \angle COB$ don’t overlap each other, which means that $\angle AOC\ \text{and}\ \angle COB$ are adjacent angles.
Complementary angles are the pair of adjacent angles in which the sum of two angles is equal to 90 degree.
$\angle COB+\angle BOA=90$, 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.
$\angle AOB+\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, $\angle AOB=90{}^\circ $ and $\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 $\angle AOB+\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.
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 $\angle AOC\ \text{and}\ \angle COB$ in which they both have side OC as common also vertex O is common in both. From the figure it is clear that $\angle AOC\ \text{and}\ \angle COB$ don’t overlap each other, which means that $\angle AOC\ \text{and}\ \angle COB$ are adjacent angles.
Complementary angles are the pair of adjacent angles in which the sum of two angles is equal to 90 degree.
$\angle COB+\angle BOA=90$, 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.
$\angle AOB+\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, $\angle AOB=90{}^\circ $ and $\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 $\angle AOB+\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.
Recently Updated Pages
Fill in the blanks with suitable prepositions Break class 10 english CBSE
Fill in the blanks with suitable articles Tribune is class 10 english CBSE
Rearrange the following words and phrases to form a class 10 english CBSE
Select the opposite of the given word Permit aGive class 10 english CBSE
Fill in the blank with the most appropriate option class 10 english CBSE
Some places have oneline notices Which option is a class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
Which are the Top 10 Largest Countries of the World?
Which is the longest day and shortest night in the class 11 sst CBSE
What is the definite integral of zero a constant b class 12 maths CBSE
Name five important trees found in the tropical evergreen class 10 social studies CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE