Question

find the measure of ∠lnh.
m∠lnh = □°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle LNH$ and $\angle GM I$ are vertical angles. So, $3x + 17=5x - 21$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $17 = 2x-21$.
Add 21 to both sides: $17 + 21=2x$, so $38 = 2x$.
Divide both sides by 2: $x = 19$.

Step3: Find the measure of $\angle LNH$

Substitute $x = 19$ into the expression for $\angle LNH$ which is $3x + 17$.
$3\times19+17=57 + 17=74$.

Answer:

$74$