Answer:
D. x = 10, m<TRS = 60
Step-by-step explanation:
1. Approach
To solve this problem, one will set up an equation to model the problem. The problem gives that the sum of two angles (m<QRT and m<TRS) equals the third angle (m<QRS). Additionally, the measure of one of the angles is given (m<QRS = 122), and the expression for the values of the other two angles are given, (m<QRT = 7x - 8), (m<TRS = 6x). One can form an equation, and solve it to find the unknown. Finally, one can then substitute the values of the unknown, into the expression to find the measure of the angle.
2. Solve for (x)
One can set up an equation based on the given information, then solve the equation.
m<QRT + m<TRS = m<QRS
Substitute,
(7x - 8) + (6x) = 122
Simplify
7x - 8 + 6x = 122
13x - 8 = 122
Inverse operations
13x - 8 = 122
+8 +8
13x = 130
/13 /13
x = 10
3. Find (m<TRS)
Now that one has the value of (x), one can substitute the value into the given expression for the (m<TRS), and solve to find the value.
m<TRS = 6x
x = 10
m<TRS = 6(10)
m<TRS = 60
