Question

The angle bisector of ∠ABC is BP−→−

. If m∠ABP = 6n, what is m∠ABC?
A. 12
B. 3n
C. 12n
D. 36n2

Answer 1

To find the measure of angle ABC, we can use the angle bisector theorem. Given that m∠ABP = 6n, we can let x = m∠ABC. Simplifying the equation, we find that m∠ABC = 0. The answer is A. 12.

Step-by-step explanation:

To find the measure of angle ABC, we can use the angle bisector theorem. According to this theorem, the angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. In this case, since the angle bisector is BP, we can say that AB/BP = AC/CP. Let's use this information to find the measure of angle ABC.

Given that m∠ABP = 6n, we can let x = m∠ABC. Since the measure of an angle is equal to the sum of its two adjacent angles, we have:

m∠ABP + m∠PBC + m∠ABC = 180°

6n + m∠PBC + x = 180°

Now, since ∠ABP and ∠PBC are adjacent angles, their measures add up to 180°:

6n + 180° - x + x = 180°

Simplifying the equation:

6n + 180° = 180°

6n = 0

n = 0

Therefore, m∠ABC = x = 0. The answer is A. 12.