Lines and Angles

i) They have a common vertex

ii) They have a common arm, and

iii) Their other arms lie on the opposite sides of the common arm.

Here, ∠ AOC and ∠BOC have the common vertex O. Also, they have a common arm OC and other arms OB and OA.

So, ∠AOC and ∠BOC are adjacent angles.

Here, OA and OB are two opposite rays and ∠AOC and ∠BOC are the adjacent angles. Therefore, ∠AOC and ∠BOC form a linear pair.

∠AOC + ∠BOC = 180

Here, AB and CD are intersecting lines and intersection point is O. So 4 angles are formed. Angles ∠1 and ∠3 form a pair of vertically opposite angles; while ∠2 and ∠4 form another pair of vertically opposite angles.

∠1 and ∠2 form a linear pair.

∠1 + ∠2 = 180

⇒ ∠1 = 180 - ∠2

Also ∠2 and ∠4 form a linear pair.

∠2 + ∠4 = 180

⇒ ∠3 = 180 - ∠2

So from the above, its clear that

∠1 = ∠3

Similarly, ∠2 = ∠4

In the given figure, O is the common point.

If you find the measures of these angles 1,2,3 and 4 then it will be

∠1 + ∠2 + ∠3 + ∠4 = 360

• Point

• Lines

• Angles

• Lines and Angles

• Complementary angles

• Supplementary angles

• Vertically Opposite Angles

• Linear Pair Angles

• Adjacent Angles

• Parallel Lines

• Solved Problems on Intersecting Lines

• Solved Problems on Parallel Lines