Question

hi Ms or Mr I'm kind of stuck here with this problem could you please help me with this?

Answer 1

x=13

$\measuredangle PQR=150$

Explanation

Step 1

Let

$\begin{gathered} \measuredangle PQS=16 \\ \measuredangle SQR=9x+17 \\ \measuredangle PQR=12x-6 \\ \\ \end{gathered}$

Step 2

by the graph

$\measuredangle\text{PQS}+\measuredangle SQR=\measuredangle PQR$

replace

$\begin{gathered} 16+9x+17=12x-6 \\ \end{gathered}$

Step 3

Finally, solve for x

$\begin{gathered} 16+9x+17=12x-6 \\ 9x+33=12x-6 \\ 9x-12x=-6-33 \\ -3x=-39 \\ x=\frac{-39}{-3} \\ x=13 \end{gathered}$

Step 4

to find

$\begin{gathered} \measuredangle PQR=12x-6=12\cdot13-6=156-6=150 \\ \measuredangle PQR=150 \\ \end{gathered}$

I hope this helps you