Question

A same side interior angle of two parallel lines is 20° less than the other same side interior angle. Find the measures of these two angles.

Answer 1

The measures of the two angles are 80 and 100

Explanation:

Let
`m_1` and
`m_2` represent the two angles such that

`m_1 = m_2 - 20`

Required

Find
`m_1` and
`m_2`

The two angles of a same-side interior angle of parallel lines add up to 180;

This implies that

`m_1 + m_2 = 180`

Substitute
`m_2 - 20` for
`m_1`

`m_1 + m_2 = 180` becomes

`m_2 - 20 + m_2 = 180`

Collect like terms

`m_2 + m_2 = 180 + 20`

`2m_2 = 180 + 20`

`2m_2 = 200`

Divide both sides by 2

`(2m_2)/(2) = (200)/(2)`

`m_2 = (200)/(2)`

`m_2 = 100`

Recall that
`m_1 = m_2 - 20`

`m_1 = 100 - 20`

`m_1 = 80`

Hence, the measures of the two angles are 80 and 100