Angle ABC and angle EBF are a pair verical angles. The measurement of angle ABC = 3X + 8 and the measurement of angle EBF = 2X + 48. What are the measurements of angle ABC and angle EBF

Vertical angles are equal.

3x+8=2x+48
x=40 deg

so now you have x, put that in the expression for each angle (3x+8;2x+48) and you have the angles.

Angle ABC = 128

Angle EBF = 128

But thats only assuming that both angles are are equal in measurement. You can't assume vertical angles are equal in measurement unless it is specified, which in this case, they are not.

To find the measurements of angle ABC and angle EBF, we'll set up an equation since we know they are vertical angles.

Vertical angles are formed when two lines intersect. They are opposite to each other and have equal measures.

Let's set up the equation:

3X + 8 = 2X + 48

To solve for X, we'll subtract 2X from both sides of the equation:

3X - 2X + 8 = 48

Simplifying the equation gives us:

X + 8 = 48

To isolate X, we'll subtract 8 from both sides:

X = 48 - 8

X = 40

Now that we have the value of X, we can substitute it back into our original equations to find the measurements of the angles.

Angle ABC = 3X + 8 = 3(40) + 8 = 120 + 8 = 128

Angle EBF = 2X + 48 = 2(40) + 48 = 80 + 48 = 128

Therefore, the measurements of angle ABC and angle EBF are both 128 degrees.