Question

in the figure, $mangle bwh=(5n + 37)^{circ}$, $mangle whn=(4n + 21)^{circ}$, $mangle drh=(7n + 1)^{circ}$, and $mangle ryh=(2n - 3)^{circ}$. what is the value of $n$ that ensures $overleftrightarrow{bn}paralleloverleftrightarrow{yd}$? $n=\frac{71}{6}$ $n=\frac{160}{13}$ $n = 16$ $n = 18$

Explanation:

Step1: Identify corresponding - angles

When $\overleftrightarrow{BN}\parallel\overleftrightarrow{YD}$, $\angle BWH$ and $\angle DRH$ are corresponding angles and are equal. So we set up the equation $5n + 37=7n + 1$.

Step2: Solve the equation for n

Subtract $5n$ from both sides: $37 = 2n+1$. Then subtract 1 from both sides: $36 = 2n$. Divide both sides by 2: $n = 18$.

Answer:

$n = 18$