Answer:
[tex]107^\circ, 133^\circ, 20^\circ, \text{and}, 23^\circ[/tex]
Step-by-step explanation:
9. For the lines 'm' and 'n' to be parallel the sum of interior angles should be 180 degrees that is:
[tex]x+73^\circ=180^\circ[/tex]
[tex]x=107^\circ[/tex]
10. For the lines 'm' and 'n' to be parallel the alternate exterior angles should be equal that is:
[tex]147^\circ=x+14^\circ[/tex]
[tex]x=147^\circ-14^\circ[/tex]
[tex]x=133^\circ[/tex]
11. For the lines 'm' and 'n' to be parallel alternate angles should be equal that is:
[tex]180^\circ-3x=2x+20^\circ[/tex]
Solving for 'x' we get:
[tex]180^\circ-20^\circ=3x+2x[/tex]
[tex]5x=160^\circ[/tex]
[tex]x=32^\circ[/tex]
12. For the lines 'm' and 'n' to be parallel corresponding angles should be equal that is:
[tex](7x-11)^\circ=(4x+58)^\circ[/tex]
[tex]7x-4x=58^\circ+11^\circ[/tex]
[tex]3x=69^\circ[/tex]
[tex]x=\frac{69}{3}=23^\circ[/tex]
