Answer:
(x, y) = (25, 18)
Step-by-step explanation:
Use the angle sum theorem. You can write equations for the right angle and for the linear angle.
(x +11) +(3y) = 90 . . . . sum of angles making the right angle
(y +7) +90 +65 = 180 . . . . sum of angles making the linear angle
From the second equation, we have ...
y = 18 . . . . subtract 162
Substituting into the first equation gives ...
x + 11 + 3(18) = 90
x = 25 . . . . subtract 65
The values of x and y are 25 and 18, respectively.
_____
Check
VQ = 18+7 = 25
QR = 25 +11 = 36
RS = 3·18 = 54
ST = 65
The totals are 36 +54 = 90; 25 +36 +54 +65 = 180, as required.
