Question

question 4 (multiple choice worth 1 points) (01 06r mc) ray be bisects ∠abc. if m∠abe=(4x + 3)° and m∠cbe=(6x - 11)°, what is m∠abe? 62° 49° 31° 7°

Explanation:

Step1: Set up equation from angle - bisector property

Since ray BE bisects ∠ABC, then m∠ABE = m∠CBE. So, we set up the equation 4x + 3=6x - 11.

Step2: Solve for x

Subtract 4x from both sides: 3 = 6x-4x - 11, which simplifies to 3 = 2x - 11. Then add 11 to both sides: 3 + 11=2x, so 14 = 2x. Divide both sides by 2, we get x = 7.

Step3: Find m∠ABE

Substitute x = 7 into the expression for m∠ABE. m∠ABE=4x + 3=4×7 + 3=28 + 3=31°.

Answer:

31°