Question

prove the opposite angles form 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:

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Answer 2

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