Question

JL−→ bisects ∠IJK, m∠IJL=(12x−2)°, and m∠LJK=(8x+6)°. Find m∠IJL.

Answer 1

By setting up an equation based on the fact that JL bisects ∠IJK, and simplifying, we find that x equals 2. Plugging x back into the expression for m∠IJL gives us 22° as the measure of angle IJL.

Step-by-step explanation:

The question involves using the properties of an angle bisector within an angle in a geometric figure. In this case, we know that the line JL bisects ∠IJK. This means that m∠IJL and m∠LJK add up to m∠IJK. Given that m∠IJL = (12x - 2)° and m∠LJK = (8x + 6)°, we can set up an equation since an angle bisector divides an angle into two equal parts. Thus, we have:

• (12x - 2)° = (8x + 6)°

To solve for x, we equate the two expressions:

1. Subtract (8x + 6)° from both sides to get: 4x - 8 = 0
2. Add 8 to both sides to get: 4x = 8
3. Divide both sides by 4 to get: x = 2

Now that we have the value of x, we can find m∠IJL by plugging x back into the expression for m∠IJL:

m∠IJL = 12(2) - 2 = 24 - 2 = 22°.

Therefore, m∠IJL is 22°.