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} (6x)/(6)=(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} (9y)/(9)=(72)/(9) \\ y=8 \end{gathered}`

The answers are

x = 15

y = 8