Final answer:
The measure of angle ABC, when the angle bisector divides it into two angles of 6n degrees each, is 12n degrees.
Step-by-step explanation:
To solve the question, we must understand that an angle bisector divides the angle into two equal parts. If MZABP is 6n degrees, and since ZABP is the angle bisector of ABC, the measure of ABC is 12n degrees.
For angles ABP (ZABP measure) and PBC (ZPBC measure) we have:
- mABP = 6n (given)
- mPBC = 6n (equal to mABP because the bisector divides the angle equally)
Therefore, mABC = mABP + mPBC = 6n + 6n = 12n degrees.