Considering the figure:
The horizontal lines are parallel lines crossed by a transversal line, the angles with measure 3xº and 60º are corresponding angles, which means that they are congruent, then:
[tex]3xº=60º[/tex]
From this expression, you can determine the value of x, simply divide both sides by 3:
[tex]\begin{gathered} \frac{3xº}{3}=\frac{60º}{3} \\ x=20º \end{gathered}[/tex]
The value of x is 20º
Next, to determine the value of y, you have to work using the quadrilateral on the bottom:
Before you can determine the value of y, you have to determine the measure of the fourth angle of the quadrilateral, which I named "z" for explanation purposes.
The angle with measure 60º and z are supplementary angles, this means that their measures add up to 180º
[tex]60º+z=180º[/tex]
From this, you can determine the value of z:
[tex]\begin{gathered} z=180º-60º \\ z=120º \end{gathered}[/tex]
You know that the sum of the inner angles of a quadrilateral is equal to 360º, for the quadrilateral marked with red, you can express this as follows:
[tex]360º=120º+60º+135º+(5y-5)º[/tex]
Now we can determine the value of y:
-Simplify all like terms together:
[tex]\begin{gathered} 360º=120º+60º+135º-5º+5y \\ 360º=310º+5y \end{gathered}[/tex]
-Subtract 310º to both sides of the equal sign:
[tex]\begin{gathered} 360º-310º=310º-310º+5y \\ 50º=5y \end{gathered}[/tex]
-Divide both sides by 5
[tex]\begin{gathered} \frac{50º}{5}=\frac{5y}{5} \\ 10º=y \end{gathered}[/tex]
The value of y is 10º
You can determine the measure of the angle as follows:
[tex]\begin{gathered} (5y-5)º \\ (5\cdot10-5)º \\ (50-5)º \\ 45º \end{gathered}[/tex]
