Question

show that the sum of all the angles formed on the same side of a line at a given point on the line is 180° .

Answer 1

Sum of interior angles of the same side of transversal line is 180

Answer 2

Refer to attached Image

Given = AOM is a straight line and ray OP , OQ and OR stand on it

To Prove = ∠AOP + ∠POQ + ∠QOR + ∠ROM = 180

Proof = Ray OP stands on line AM

∠AOP + ∠POM = 180

∠AOP + ∠POQ + ∠QOR + ∠ROM = 180 [Explanation ∠POQ + ∠QOR + ∠ROM = ∠POM]

∠AOP + ∠POQ + ∠QOR + ∠ROM = 180

Therefore

Sum of all angles formed on same side of line AM at a point O on it is 180