Question

bd bisects ∠abc. solve for x and find m∠abc. m∠abd = 7x - 6, m∠cbd = 4x + 6

Explanation:

Step1: Set angle - equal equations

Since BD bisects ∠ABC, then m∠ABD = m∠CBD. So we set up the equation 7x - 6 = 4x+6.

Step2: Solve for x

Subtract 4x from both sides: 7x - 4x - 6=4x - 4x + 6, which simplifies to 3x - 6 = 6. Then add 6 to both sides: 3x-6 + 6=6 + 6, getting 3x = 12. Divide both sides by 3: $\frac{3x}{3}=\frac{12}{3}$, so x = 4.

Step3: Find m∠ABC

First find m∠ABD or m∠CBD. Using m∠ABD = 7x - 6 and substituting x = 4, we get m∠ABD=7×4 - 6=28 - 6 = 22. Since m∠ABC = 2m∠ABD (because of bisection), then m∠ABC = 2×22 = 44.

Answer:

x = 4, m∠ABC = 44