Given:
A figure in which a transversal line intersect two parallel lines.
[tex]m\angle 2=4x+7, m\angle 7=5x-13, m\angle 5=68[/tex] and [tex]m\angle 3=3y-2[/tex].
To find:
The value of x and y.
Solution:
We know that, if a transversal line intersect two parallel lines, then
(1) Alternate exterior angles are equal.
(2) Same sided interior angles are supplementary. So their sum is 180 degrees.
In the given figure j and k are parallel lines and l is a transversal line.
From the given figure, it is clear that,
[tex]m\angle 2=m\angle 7[/tex] (Alternate exterior angles are equal)
[tex]4x+7=5x-13[/tex]
[tex]7+13=5x-4x[/tex]
[tex]20=x[/tex]
Therefore, the value of x is 20.
Now,
[tex]\angle 3+\angle 5=180[/tex] (Same sided interior angles are supplementary)
[tex]3y-2+68=180[/tex]
[tex]3y+66=180[/tex]
[tex]3y=180-66[/tex]
[tex]y=\dfrac{180-66}{3}[/tex]
[tex]y=\dfrac{114}{3}[/tex]
[tex]y=38[/tex]
Therefore, the value of y is 38.
