Question

Find x and y so that line MR is perpendicular to line MQ

Answer 1

Since NR is perpendicular to MQ,

Since NR intersected MQ at S, then

The four angles formed between them are right angles

$m\angle NSQ=90^{\circ}$

Since

Then add them and equate the answer by 90

$\begin{gathered} 5x+x=90 \\ 6x=90 \end{gathered}$

Divide both sides by 6

$\begin{gathered} \frac{6x}{6}=\frac{90}{6} \\ x=15 \end{gathered}$

Since angle MSR = 90 degrees, then

$9y+18=90$

Subtract 18 from each side

$\begin{gathered} 9y+18-18=90-18 \\ 9y=72 \end{gathered}$

Divide both sides by 9

$\begin{gathered} \frac{9y}{9}=\frac{72}{9} \\ y=8 \end{gathered}$

The answers are

x = 15

y = 8