Question

Prove that the sum of a linear pair is 180° .

Answer 1

hi mate


your answer is in attachment

Answer 2

Answer:

Concept:

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as additional angles.

Step-by-step explanation:

Given:

Two adjacent angles are ∠AOC and ∠BOC and ∠AOC+∠BOC=180°.

Find:

Prove that the sum of a linear pair is 180°.

Solution:

Refer to the image given

OA and OB are two opposite rays.

Let OA and OB are not two opposite rays.

Then, draw a ray OE opposite to OA such that AOE is a straight line.

∠AOC+∠BOC = 180°. .....(1)

∠AOC+∠CO = 180°.   ....(2) (Linear pair)

∠AOC+∠EOC=∠AOC+∠BOC (From equation 1 and 2)

∴∠EOC=∠BOC

This is possible only if OE and OB coincide. Hence, OA and OB are two opposite rays.

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