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`

Step-by-step 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=(-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