Answer:
Number 7) x=14 and y=37
Number 8) x=28 and y=23
Explanation:
Number 7) Please see fig 1 in the attachment for naming of angle.
As per diagram line b||c and their transverse line a.
Using line and angle concepts.
[tex]\angle 1=3x[/tex] {Corresponding angles of parallel line b||c}
[tex]\angle 1+(9x+12)=180^{\circ}[/tex] {Supplementary angle of straight line}
[tex]\therefore 3x+9x+12=180[/tex]
Now combine the like term and solve for x and we get,
12x=180-12
x=14
For line a, 4y-10+3x=180 {Supplementary angle of straight line}
where, x=14
So, we get 4y-10+3(14)=180
4y=180-32
y=37
Number 8) Please see fig 2 in the attachment for naming of angles.
As per given diagram a||b||c and line d is transversal of all three line.
Using line and angle concepts.
[tex]\angle 1=3y[/tex] {Corresponding angles of parallel line a||b}
[tex]\angle 1+(5y-4)=180^{\circ}[/tex] {Supplementary angle of straight line}
3y+5y-4=180
8y=184
y=23
3y=2x+13 {Corresponding angles of parallel line b||c}
we calculated y=23 substitute into above equation and we get
3(23)=2x+13
2x=69-13
x=28
