Question

1. ray bc bisects ∠abd. draw a picture to model this situation, then find the m∠abc if m∠cbd = 4x - 10 and m∠abc = 3x + 9.

Explanation:

Step1: Use angle - bisector property

Since ray $BC$ bisects $\angle ABD$, we know that $\angle ABC=\angle CBD$. So we set up the equation $3x + 9=4x-10$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $3x + 9-3x=4x-10-3x$, which simplifies to $9=x - 10$. Then add 10 to both sides: $9 + 10=x-10 + 10$, so $x = 19$.

Step3: Find the measure of $\angle ABC$

Substitute $x = 19$ into the expression for $\angle ABC$. $\angle ABC=3x + 9$. So $\angle ABC=3\times19+9$. First, calculate $3\times19 = 57$, then $57+9=66$.

Answer:

$m\angle ABC = 66$