# CLASS-8GEOMETRY - TYPES OF ANGLES

TYPES OF ANGLES -

Two angles are called adjacent angles if they have the same vertex and a common arm and their other arms are on either side of the common arm. In the figure COB and BOA are adjacent angles. While COA and COB are not adjacent angles.

Linear Pair –

Two adjacent angles are said to form a linear pair if the sum of their measures is 180⁰. Here AOB & AOC form a linear pair because 115⁰ + 65⁰ = 180⁰

Property - If a ray OA stands on a line BC then the adjacent angles AOB & AOC form a linear pair, that is -

AOB + AOC = 180⁰

Also, the sum of all the angles at a point of a line on one side of it is 180⁰. Here  BOQ + QOP + POC = 180⁰

Complementary Angles –

Two angles are called complementary angles if the sum of their measures is 90⁰, each angle is said to be the complement of the other. For example, two angles of measures 32⁰ and 58⁰ are complementary angles.

Supplementary Angles –

Two angles are called supplementary angles if the sum of their measures is 180⁰, each angle is said to be the supplement of the other. For example, angles of measures 104⁰ and 76⁰ are supplementary angles.

Angles at a Point –

The sum of all the angles at a point, making a complete rotation, is 360⁰. In the figure, 60⁰ + 90⁰ + 90⁰ + 120⁰ = 360⁰

Vertically Opposite Angles -

When two straight lines AB & CD intersect at the point 0 then the pairs (1) ∠AOD and ∠COB and (2) ∠AOC and ∠BOD are called vertically opposite angles.

Property -  If two lines intersect then the vertically opposite angles so formed are equal.

In the figure, ∠AOD = ∠COB and ∠AOC = ∠BOD