Answer:
60 degrees
Step-by-step explanation:
The sum of interior angles of a hexagon is 720 degrees, so:
[tex](180-m_1)+(180-m_2)+(180-m_3)+(180-m_4)+(180-m_5)+(180-m_6)=720[/tex]
We know that angle 6 is 90 degrees, so:
[tex](180-m_1)+(180-m_2)+(180-m_3)+(180-m_4)+(180-m_5)+90=720\\(180-m_1)+(180-m_2)+(180-m_3)+(180-m_4)+(180-m_5)=630\\900-m_1-m_2-m_3-m_4-m_5=630\\-m_1-m_2-m_3-m_4-m_5=-270\\m_1+m_2+m_3+m_4+m_5=270[/tex]
We will rewrite the definition of angle 4:
[tex]m_4=m_3+10\\m_4-10=m_3[/tex]
And we will start a substitution madness:
[tex]m_1+m_2+m_3+m_4+m_5=270\\m_3+m_3+m_3+m_4+m_5=270\\(m_4-10)+(m_4-10)+(m_4-10)+m_4+m_5=270\\3m_4-30+m_4+m_5=270\\3m_5-30+m_5+m_5=270[/tex]
For the sake of simplicity, we will replace angle 5 as x:
[tex]3x-30+x+x=270\\5x-30=270\\5x=300\\x=60[/tex]
And don't forget the degree sign!
