Question

question 3 (multiple choice worth 1 points) (01 06r mc) ray il bisects angle hij. if m∠hil=(6x - 7)° and m∠jil=(5x + 4)°, what is m∠jil? 118° 59° 44° 11°

Explanation:

Step1: Use angle - bisector property

Since ray IL bisects angle HIJ, then \(m\angle HIL=m\angle JIL\). So we set up the equation \(6x - 7=5x + 4\).

Step2: Solve for x

Subtract \(5x\) from both sides of the equation: \(6x-5x - 7=5x-5x + 4\), which simplifies to \(x-7 = 4\). Then add 7 to both sides: \(x=4 + 7=11\).

Step3: Find \(m\angle JIL\)

Substitute \(x = 11\) into the expression for \(m\angle JIL\). \(m\angle JIL=(5x + 4)^{\circ}\), so \(m\angle JIL=5\times11+4=55 + 4=59^{\circ}\).

Answer:

59°