Question

bd bisects ∠abc. solve for x and find m∠abc. m∠abd = 5x - 8, m∠cbd = 2x + 7

Explanation:

Step1: Set up equation

Since BD bisects ∠ABC, then m∠ABD = m∠CBD. So we set up the equation 5x - 8=2x + 7.

Step2: Solve for x

Subtract 2x from both sides: 5x-2x - 8=2x-2x + 7, which simplifies to 3x - 8=7. Then add 8 to both sides: 3x-8 + 8=7 + 8, getting 3x=15. Divide both sides by 3: $\frac{3x}{3}=\frac{15}{3}$, so x = 5.

Step3: Find m∠ABD

Substitute x = 5 into the expression for m∠ABD: m∠ABD=5(5)-8=25 - 8=17.

Step4: Find m∠ABC

Since m∠ABC = 2m∠ABD (because of bisection), then m∠ABC=2×17 = 34.

Answer:

x = 5, m∠ABC = 34