Question

Theorem : The Opposite angles formed by two intersecting lines are of equal measures. Given: Line AB and Line CD intersect at point O such that A - O - B, C - O- D​

Answer 1

Answer:

The Opposite angles formed by two intersecting lines are of equal measures

Step-by-step explanation:

Line AB and Line CD intersect at point O such that A - O - B, C - O- D​

∠AOC = x

∠BOD = y

to be proved  x = y

AB is a straight line

=> ∠AOC  + ∠COB  =  180°

=> x + ∠COB  =  180°

=> ∠COB = 180° - x

CD is  a straight line

=> ∠COB + ∠BOD = 180°

=> ∠COB + y = 180°

=> y = 180° - ∠COB

putting ∠COB = 180° - x

=> y = 180° -  ( 180° - x)

=> y = x

=> ∠BOD = ∠AOC

The Opposite angles formed by two intersecting lines are of equal measures