Question

find the measure of \\( \angle l n h \\).

\\( m \angle l n h= \\) \\( \circ \\)

Explanation:

Step1: Use the property of parallel lines and corresponding angles

Since the lines are parallel, \(5x - 21=3x + 17\) (corresponding angles are equal).

$$\begin{align*} 5x-3x&=17 + 21\\ 2x&=38\\ x&=19 \end{align*}$$

Step2: Find the measure of \(\angle LNH\)

Substitute \(x = 19\) into \(3x+17\).
\(3\times19 + 17=57+17 = 74\)

Answer:

\(74\)