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