Answer:
x = 14, y = 37
Step-by-step explanation:
The angle vertically opposite (4y-10) is also a corresponding angle to (9x + 12) so that means that angles (4y-10) and (9x+12) are equal.
4y-10 = 9x+12 -----Equation 1
You also know that (4y-10) and 3x add up to 180° since they both lie on a straight line.
4y-10+3x = 180 -----Equation 2
From the above equation, I'm going to isolate (4y-10) so that I know a value that I can substitute in Equation 1.
4y-10 = 180-3x -----Equation 3
Substitute 4y-10 = 180-3x into Equation 1.
4y-10 = 9x+12
180-3x = 9x+12
Put the like terms together.
180-12 = 9x+3x
Evaluate.
12x = 168
Find x.
x = 168 ÷ 12
x = 14
Subsitite x = 14 into Equation 3.
4y-10 = 180-3x
= 180-3(14)
= 180-42
= 138
Isolate 4y.
4y = 138+10
= 148
Find y.
y = 148 ÷ 4
y = 37
