Answer:
[tex]m_2= 115[/tex]
[tex]m_3 = 65[/tex]
[tex]m_4 = 115[/tex]
[tex]m_5 = 65[/tex]
[tex]m_6 = 115[/tex]
[tex]m_7 = 65[/tex]
[tex]m_8 = 115[/tex]
Step-by-step explanation:
See attachment for complete question.
Given
[tex]m_1 = 65[/tex]
Required
Determine the missing angles
m1 and m2 are supplementary angles.
Meaning that:
[tex]m_1 +m_2 = 180[/tex]
Substitute 65 for m1
[tex]65 +m_2 = 180[/tex]
[tex]m_2= 180 - 65[/tex]
[tex]m_2= 115[/tex]
m1 and m3 are vertically opposites.
m2 and m4 are also vertically opposites.
So:
[tex]m_3 = m_1[/tex]
and
[tex]m_4 = m_2[/tex]
i.e.
[tex]m_3 = 65[/tex]
[tex]m_4 = 115[/tex]
When parallel lines are traversed by a line, the corresponding angles are equal.
This means that:
[tex]m_5 = m_1[/tex]
[tex]m_6 = m_2[/tex]
[tex]m_7 = m_3[/tex]
[tex]m_8 = m_4[/tex]
Because they are all corresponding angles.
So:
[tex]m_5 = 65[/tex]
[tex]m_6 = 115[/tex]
[tex]m_7 = 65[/tex]
[tex]m_8 = 115[/tex]
