SOLUTION: This is a problem on my Geometry Study guide for the final exam: SR is a diameter of circle M. Measurement of angle RMT = (x+5)degrees, measurement of angle UMR = (x+10)degrees,

Question 615651: This is a problem on my Geometry Study guide for the final exam:
SR is a diameter of circle M.
Measurement of angle RMT = (x+5)degrees,
measurement of angle UMR = (x+10)degrees, and
measurement of angle SMT = (3x-5)degrees.
What is the value of x?
The answer is 45 but I do not know how to solve this problem.
Thank you
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
This is a problem on my Geometry Study guide for the final exam:
SR is a diameter of circle M.
Measurement of angle RMT = (x+5)degrees,
measurement of angle UMR = (x+10)degrees, and
measurement of angle SMT = (3x-5)degrees.
What is the value of x?
The answer is 45 but I do not know how to solve this problem.
Thank you

It's best to draw a diagram, so everything will be clearer.

Since this is circle M, then M will be the center-point of the circle. This means that the diameter is SMR, since a diameter goes through the center of a circle

Since angle RMT = , and angle SMT angle = , we can say that:

x + 5 + 3x � 5 = 180

x + 3x + 5 - 5 = 180

4x = 180

x = , or

Angle UMR is insignificant, regardless of where it's drawn.

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