Question

applying the angle addition postulate
the measure of angle jkl can be represented using the expression 3x + 5.
what is the degree measure of ∠jkl?

Explanation:

Step1: Apply Angle Addition Postulate

The Angle Addition Postulate states that \( \angle JKL = \angle JKM + \angle MKL \). From the diagram, \( \angle JKM = 45^\circ \) and \( \angle MKL = x^\circ \), and \( \angle JKL = 3x + 5 \). So we set up the equation:

$$ 3x + 5 = 45 + x $$

Step2: Solve for \( x \)

Subtract \( x \) from both sides:

$$ 3x - x + 5 = 45 + x - x $$

$$ 2x + 5 = 45 $$

Subtract 5 from both sides:

$$ 2x + 5 - 5 = 45 - 5 $$

$$ 2x = 40 $$

Divide both sides by 2:

$$ x = \frac{40}{2} = 20 $$

Step3: Find \( \angle JKL \)

Substitute \( x = 20 \) into \( 3x + 5 \):

$$ 3(20) + 5 = 60 + 5 = 65 $$

Answer:

65