Answer:
x = 27, and y = 47.
Explanation:
AB is a line, so the measures of the angles measuring
2x + 1, 3x + 10, and 8/9 x + 10
add to 180 degrees. We can use that fact to find x.
2x + 1 + 3x + 10 + 8/9 x + 10 = 180
Add like terms on the left side except for the faction.
5x + 8/9 x + 21 = 180
Multiply both sides by 9.
45x + 8x + 189 = 1620
Add like terms on the left side. Subtract 168 from both sides.
53x = 1431
Divide both sides by 53.
x = 27
The angle measuring 3x + 10 is vertical with the angle that is made up of the measures y - 3 and y. Therefore, the sum of the measures y - 3 and y equals the measure 3x + 10. We know x, so we can find 3x + 10.
3x + 10 = 3(27) + 10 = 91
Now we set the sum of y - 3 and y equal to 91 and solve for y.
y - 3 + y = 91
2y - 3 = 91
2y = 94
y = 47
x = 27, and y = 47.