Question

BD bisects ABC, měABC = (4x - 12), and m&DBC = 24º. (Hint: It may be helpful to draw a diagram)

a. Solve for x.
A. x = 9
B. x = 12
C. x = 15
D. x = 18

Answer 1

To solve for x, set up the equation 24 = (4x - 12) since angle BD bisects angle ABC. Add 12 to both sides and divide by 4, finding that x equals 9.

Step-by-step explanation:

The student is asking to solve for the variable x in the context of geometry where angle BD bisects angle ABC, and the measure of angle ABC is given as (4x - 12) degrees, and the measure of angle DBC is given as 24 degrees. Since BD bisects angle ABC, the two angles created (mäABC) and m&DBA) will each be equal to 24 degrees. Therefore:

• Set up the equation: 24 = (4x - 12)
• Add 12 to both sides: 24 + 12 = 4x
• Simplify: 36 = 4x
• Divide both sides by 4: x = 9

Therefore, the value of x is 9.