Question

BH bisects angle ABC, solve for x. A) x = 11 B) x = 12 C) x = 15 D) x = 7

Answer 1

Using the Angle Bisector Theorem, we can solve for x in the given triangle.

Step-by-step explanation:

Given that BH bisects angle ABC, we can use the Angle Bisector Theorem to find the value of x:

The Angle Bisector Theorem states that the ratio of the lengths of the segments formed by the angle bisector is equal to the ratio of the lengths of the opposite sides of the triangle.

In this case, we have AB/BC = AH/HC. Since BH bisects angle ABC, we know that AH = HC. Therefore, AB/BC = 1.

Since AB = x + 3 and BC = 2x - 3, we can set up the equation:

x + 3 / 2x - 3 = 1

Solving the equation, we get x = 12. Therefore, the correct answer is B) x = 12.

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