Question

find the measure of ∠loi.
m∠loi =
°
submit

Explanation:

Step1: Identify the relationship

Since lines \( KM \) and \( LJ \) are parallel (assumed from the diagram with equal arrows), and \( HI \) is a transversal, the angles \( (5x + 19)^\circ \) and \( (9x - 5)^\circ \) are alternate exterior angles, so they are equal.

$$ 5x + 19 = 9x - 5 $$

Step2: Solve for \( x \)

Subtract \( 5x \) from both sides:

$$ 19 = 4x - 5 $$

Add 5 to both sides:

$$ 24 = 4x $$

Divide by 4:

$$ x = 6 $$

Step3: Find \( m\angle LOI \)

Substitute \( x = 6 \) into \( 9x - 5 \):

$$ 9(6) - 5 = 54 - 5 = 49 $$

Answer:

\( 49 \)