Question

ae is an angle bisector of ∠bac. if m∠bae = x + 30 and m∠eac = 3x - 10, determine the value of x.

Explanation:

Step1: Use angle - bisector property

Since AE is an angle bisector of ∠BAC, then m∠BAE = m∠EAC. So we set up the equation $x + 30=3x - 10$.

Step2: Solve the equation for x

First, subtract x from both sides: $30 = 3x - x-10$. Simplify to get $30 = 2x - 10$. Then add 10 to both sides: $30 + 10=2x$, which gives $40 = 2x$. Finally, divide both sides by 2: $x=\frac{40}{2}=20$.

Answer:

20