The measures of the angles of �qrs are m∠q = 2x + 4, m∠r = 4x − 12, and m∠s = 3x + 8. qr = y + 9, rs = 2y − 7, and qs = 3y − 13. the perimeter of �qrs is

Let QRS be a triangle with angles Q, R and S. The sum of triangle angles measures is equal to 180^°, so
2x+4+4x-12+3x+8=180^°, 9x=180^° and x=20^°.
m∠Q=2x+4=44^°,
m∠R=4x-12=68^°,
m∠S=3x+8=68^°.
The triangle QRS is isoscales, because ∠R=∠S, thus QS=QR are equal sides and SR is basis. 
QR=y+9 and QS=3y-13, then y+9=3y-13, 2y=22 and y=11.
QR=11+9=20=QS, RS=2y-7=22-7=15.
The perimeter of triangle QRS is QS+QR+RS=20+20+15=55 units.

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