Answer:
x=6
y=128
Step-by-step explanation:
in my diagram shown in red the angles are corresponding. This means they are equal. Equate them both in an equation:
[tex]7x + 4 = 5x + 16[/tex]
subtract 5x on both sides
[tex]7x - 5x + 4 = 16[/tex]
subtract 4 on both sides
[tex]7x - 5x = 16 - 4[/tex]
collect like terms
[tex]2x = 12[/tex]
divide 2 on both sides giving
[tex]x = 6[/tex]
substitute x=6 into any of the equations 5x+16 or 7x+4 since both of them are the same. I'll use 5x+16
5(6)+16=46 degrees
since opposite angles are equal the angle is 46 degrees shown in green on my drawing
to work out y interior angles are equal to 180: equate 46 and y+6 to 180:
[tex]46 + y + 6 = 180[/tex]
subtract 6 and 46 on both sides
[tex]y = 180 - 46 - 6[/tex]
[tex]y = 128[/tex]
so y is 128
