In the diagram below of triangle R, S, TRST, UU is the midpoint of start overline, R, T, end overline
RT
and VV is the midpoint of start overline, S, T, end overline
ST
. If mangle, T, S, R, equals, minus, 5, x, plus, 93∠TSR=−5x+93, and mangle, T, V, U, equals, 82, plus, 6, x∠TVU=82+6x, what is the measure of angle, T, S, R∠TSR?
Since U is the midpoint of RT, we know that UT = TR. Similarly, since V is the midpoint of ST, we know that SV = ST.
From triangle TVU, we have:
TS = TV + VS = TV + ST
ST = TS - TV
Since UT = TR and SV = ST, we can rewrite the above equations:
ST = TR - TV
We know that angle TSR and angle TVU are supplementary angles, so:
TSR + TVU = 180
-5x + 93 + 82 + 6x = 180
x + 175 = 180
x = 5
Now we can plug x back into -5x + 93 to find TSR:
-5(5) + 93 = 93 - 25 = 68
Therefore, the measure of angle TSR is 68 degrees.