Two angles are said to be adjacent if they share a common arm and a common vertex between them. In simple words angles that are formed side by side are called adjacent angles. One of the main features of adjacent angles is that they do not overlap. Angles that are not adjacent are called nonadjacent angles.
Adjacent Angles
The figure above shows two adjacent angles having a common side and a common vertex.
Are Adjacent Angles Complementary or Supplementary
Adjacent angles can be both complementary and supplementary. When the two angles add up to 90° it is called adjacent complementary angles, whereas when the two angles add up to 180° it is called adjacent supplementary angles. Two adjacent supplementary angles form a linear pair.
To identify whether the angles are adjacent or not, we must remember its basic properties that are given below:
They should share a common arm between them
They should share a vertex between them
They should not overlap
They should have a non-common arm on both the sides of the common arm
Are Adjacent Angles Congruent
Adjacent angles are congruent only when their common side bisects their sum. This happens when:
A right angle is bisected to from two adjacent angles each measuring 45°
A straight angle is bisected to from two adjacent angles where each of them is a right angle measuring 90°
Solve to find the adjacent angle marked x. Given that ∠AOB = 120° and ∠AOC = 80°
Solution:
Given ∠AOB = 120° and ∠AOC = 80° Since, ∠AOC and ∠COB are adjacent angles Thus, ∠AOC + ∠COB = ∠AOB, here ∠COB = x 80° + x = 120° x = 120° – 80° x = 40°
Which one of the pairs of angles given below is adjacent in the given figure.
Solution:
∠AOP and ∠POQ, ∠POQ and ∠QOR, ∠QOR and ∠ROB are three adjacent pairs of angles in the given figure.
Which one of the pairs of angles given below are adjacent? Give reasons for you answer.
Solution:
a) ∠1 and ∠2 are adjacent angles because both share a common side and a common vertex b) ∠1 and ∠2 are nonadjacent angles because they don’t share a common side c) ∠1 and ∠2 are nonadjacent angles because they don’t have a common vertex d) ∠1 and ∠2 are nonadjacent angles because they overlap each other e) ∠1 and ∠2 are nonadjacent angles because they don’t share a common vertex
Examples in Real Life
An opened book with a page in between them
Hands of a clock showing 3PM and the seconds hand pointing towards the digit 2
Angles formed at the center of a cartwheel
A sliced pizza or a cake
Last modified on August 3rd, 2023
One thought on “Adjacent Angles”
Didn’t know absolutely nothing about the adjacent angles
Solve to find the adjacent angle marked x. Given that ∠AOB = 120° and ∠AOC = 80°
Which one of the pairs of angles given below is adjacent in the given figure.
Which one of the pairs of angles given below are adjacent? Give reasons for you answer.
Didn’t know absolutely nothing about the adjacent angles
until looking here
Thanks!