Question

А7. Given mKJM = 170°, find the value of x.Rк(13x-2) L(6X+1)M

Answer 1

7.

From the diagram, we can conclude:

$\begin{gathered} m\angle KJM=m\angle KJL+m\angle LJM \\ where \\ m\angle KJM=170 \\ m\angle KJL=13x-2 \\ m\angle LJM=6x+1 \end{gathered}$

Therefore:

$170=13x-2+6x+1$

Add like terms:

$170=19x-1$

Solve for x:

$\begin{gathered} 170+1=19x \\ 19x=171 \\ x=\frac{171}{19} \\ x=9 \end{gathered}$

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8-9

From the diagram we can conclude:

$\begin{gathered} m\angle SRT=m\angle PRQ \\ m\angle PRS=m\angle QRT=100 \\ m\angle PRS+m\angle QRT+m\angle SRT+m\angle PRQ=360 \\ so\colon \\ 100+100+2m\angle SRT=360 \\ 2m\angle SRT=360-200 \\ 2m\angle SRT=160 \\ m\angle SRT=\frac{160}{2} \\ m\angle SRT=80 \end{gathered}$

So:

$\begin{gathered} m\angle RPQ+m\angle PQR+m\angle PRQ=180 \\ m\angle RPQ+80+60=180 \\ m\angle RPQ=180-140 \\ m\angle RPQ=40 \end{gathered}$

Therefore:

$\begin{gathered} m\angle RPQ=40 \\ m\angle PRS=100 \end{gathered}$