Answer: angle V = 41 degrees (choice B)
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Explanation:
We're told that RS = ST = RT. This means triangle RST has all three sides equal to one another. This triangle is equilateral. Each interior angle is 60 degrees. This is because each angle is y, and y+y+y = 180.
Since each angle of triangle RST is 60 degrees, this means angle STR is 60 degrees.
Let z be the measure of angle UTV. Note how
(angleSTR)+(angleUTV) = 180
60+z = 180
z = 180-60
z = 120
Making angle UTV to be 120 degrees
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Now we can focus on triangle UTV since we have expressions for each interior angle
Add up those angles, set the sum equal to 180, solve for x
U+T+V = 180
(4x-9)+(120)+(5x+6) = 180
9x+117 = 180
9x = 180-117
9x = 63
x = 63/9
x = 7
Use that x value to find the missing angle measures
angle U = 4x-9 = 4*7-9 = 28-9 = 19 degrees
angle V = 5x+6 = 5*7+6 = 35+6 = 41 degrees
Note how
U+T+V = 19+120+41 = 180
which helps confirm our answer.
