Question

find the measure of ∠lnh.

Explanation:

Step1: Identify angle - relationship

Since the two horizontal lines are parallel, the angles $(5x - 21)^{\circ}$ and $(3x + 17)^{\circ}$ are corresponding angles and are equal.
$5x-21 = 3x + 17$

Step2: Solve for x

Subtract $3x$ from both sides:
$5x-3x-21=3x - 3x+17$
$2x-21 = 17$
Add 21 to both sides:
$2x-21 + 21=17 + 21$
$2x=38$
Divide both sides by 2:
$x=\frac{38}{2}=19$

Step3: Find the measure of $\angle LNH$

Substitute $x = 19$ into the expression for $\angle LNH=(3x + 17)^{\circ}$
$\angle LNH=3\times19+17$
$=57 + 17$
$=74^{\circ}$

Answer:

$74^{\circ}$