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


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 = {{{(x + 5)^o}}}, and angle SMT angle = {{{(3x - 5)^o}}}, we can say that: 


x + 5 + 3x – 5 = 180


x + 3x + 5 - 5 = 180


4x = 180


x = {{{180/4}}}, or {{{highlight_green(45^o)}}}


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


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