Question 849553
you have 2 lines that cross.

the left angle formed is equal to 3x + 8
the right angle formed is equal to 5x - 20.
the bottom angle formed is equal to 5x + 4y


since the lines are crossed, the opposite angles to each other are equal.


this means that:


3x + 8 = 5x - 20


solve for x to get x = 14 degrees.


the angle on the left side will be equal to 3(14) + 8 = 50 degrees.
the angle on the right side will be equal to 5(14) - 20 = 50 degrees.
this is at it should be since the angles are equal to each other.


since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.


since those 2 angles are equal, then each one must be equal to 130 degrees.


one of those angles is equal to 5x + 4y.


you get 5x + 4y = 130


since x was already found to be 14, replace x with 14 to get:


5(14) + 4y = 130


solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.


when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.


your answers are:


x = 14 degrees
y = 15 degrees
2 of the angles measure 50 degrees each.
2 of the angles measure 130 degrees each.