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?
R
S
T
U
V
Answer
Attempt 2 out of 2
m, angle, T, S, R, equalsm∠TSR=
degrees
∘
To find the measure of angle TSR, we can use the fact that in a triangle, the sum of all angles is 180 degrees.
Since U is the midpoint of RT, by the midpoint theorem, we know that angle TUV is equal to angle TVS. This means:
m∠TVS = m∠TVU = 82 + 6x
Similarly, since V is the midpoint of ST, by the midpoint theorem, we know that angle VUT is equal to angle VUS. This means:
m∠VUS = m∠VUT = 82 + 6x
Now, adding up all the angles in triangle TRS, we have:
m∠TSR + m∠VUS + m∠VUT = 180
-5x + 93 + (82 + 6x) + (82 + 6x) = 180
-5x + 93 + 82 + 6x + 82 + 6x = 180
-5x + 6x + 6x = 180 - 93 - 82 - 82
7x = 3
x = 3/7
Now, substitute the value of x back into the equation for angle TSR:
m∠TSR = -5x + 93
m∠TSR = -5(3/7) + 93
m∠TSR = -15/7 + 93
m∠TSR = (93*7 - 15) / 7
m∠TSR = (651 - 15) / 7
m∠TSR = 636 / 7
m∠TSR = 90 degrees
Therefore, the measure of angle TSR is 90 degrees.