Answer:
The measures of the two angles are 80 and 100
Step-by-step explanation:
Let [tex]m_1[/tex] and [tex]m_2[/tex] represent the two angles such that
[tex]m_1 = m_2 - 20[/tex]
Required
Find [tex]m_1[/tex] and [tex]m_2[/tex]
The two angles of a same-side interior angle of parallel lines add up to 180;
This implies that
[tex]m_1 + m_2 = 180[/tex]
Substitute [tex]m_2 - 20[/tex] for [tex]m_1[/tex]
[tex]m_1 + m_2 = 180[/tex] becomes
[tex]m_2 - 20 + m_2 = 180[/tex]
Collect like terms
[tex]m_2 + m_2 = 180 + 20[/tex]
[tex]2m_2 = 180 + 20[/tex]
[tex]2m_2 = 200[/tex]
Divide both sides by 2
[tex]\frac{2m_2}{2} = \frac{200}{2}[/tex]
[tex]m_2 = \frac{200}{2}[/tex]
[tex]m_2 = 100[/tex]
Recall that [tex]m_1 = m_2 - 20[/tex]
[tex]m_1 = 100 - 20[/tex]
[tex]m_1 = 80[/tex]
Hence, the measures of the two angles are 80 and 100
