Explanation:
To find the measure of angle ABE (mABE), you need to set up an equation based on the given expressions for mABE and mEBF.
Given:
mABE = 2n + 7
mEBF = 4n - 13
Since both angles ABE and EBF are parts of the same angle, you can set up an equation:
mABE + mEBF = 180 degrees (because they are supplementary angles)
Now, substitute the expressions for mABE and mEBF into the equation:
(2n + 7) + (4n - 13) = 180
Combine like terms:
2n + 4n + 7 - 13 = 180
6n - 6 = 180
Add 6 to both sides to isolate 6n:
6n = 180 + 6
6n = 186
Now, divide by 6 to solve for n:
n = 186 / 6
n = 31
Now that you have found the value of n, you can find mABE by substituting it into the expression for mABE:
mABE = 2n + 7
mABE = 2(31) + 7
mABE = 62 + 7
mABE = 69
So, the measure of angle ABE (mABE) is 69 degrees.