Question

Given: angle one and angle two forms a linear pair; angle one and angle three are supplementary

Prove: angle two is congruent to angle three
Step by step please, that would be great

Answer 1

Explanation:

angle 1 & angle 2 are linear pair. That means both the angles form a straight angle (or 180°). Hence ,

`m(1) + m(2) = 180`

`= > m(1) = 180 - m(2)`

Also it's given that angle 1 & angle 3 are supplementary. It means that their sum will be equal to 180° . So ,

`m(1) + m(3) = 180`

Putting the value of m(1) in above eqn. gives :-

`m(1) + m(3) = 180`

`= > 180 - m(2) + m(3) = 180`

`= > - m(2) + m(3) = 180 - 180`

`= > m(3) - m(2) = 0`

`= > m(3) = m(2)`