Question

identify the angle relationship before writing the equation. if m∠knm=(8x - 5)° and m∠mnj=(4x - 19)°, find the measure of ∠knm.

Explanation:

Step1: Identify angle relationship

$\angle KNM$ and $\angle MNJ$ are vertical - angles, so $\angle KNM=\angle MNJ$.
$8x - 5=4x + 19$

Step2: Solve for $x$

Subtract $4x$ from both sides:
$8x-4x - 5=4x-4x + 19$
$4x-5 = 19$
Add 5 to both sides:
$4x-5 + 5=19 + 5$
$4x=24$
Divide both sides by 4:
$x = 6$

Step3: Find measure of $\angle KNM$

Substitute $x = 6$ into the expression for $\angle KNM$:
$m\angle KNM=8x - 5=8\times6-5=48 - 5=43^{\circ}$

Answer:

$43^{\circ}$