Question

I need help with numbers 3, 4, and 5 please

Answer 1

3) We can see in the image that the sum of the angles PQS and SQR will be the angle PQR. So we have that:

`\begin{gathered} \text{PQS}+\text{SQR}=\text{PQR} \\ 13x+4+10x-1=141 \\ 13x+10x=141-4+1 \\ 23x=138 \\ x=6 \\ \text{PQS}=13x+4=13\cdot6+4=78+4=82\degree \\ \text{SQR}=10x-1=10\cdot6-1=60-1=59\degree \end{gathered}`

4) The angle DEF is the sum of the angles DEG and GEF, so we have that:

5) The angle JKL is the sum of the angles JKM and MKL, so we have that:

`\begin{gathered} \text{JKM}+\text{MKL}=\text{JKL} \\ 43+8x-20=10x-11 \\ 8x-10x=-11-43+20 \\ -2x=-34 \\ x=17 \\ \text{MKL}=8x-20=8\cdot17-20=136-20=116\degree \\ \text{JKL}=10x-11=10\cdot17-11=170-11=159\degree \end{gathered}`