Question

In Triangle RST, SR < ST and RT > ST. If angle R = 2x + 10 and angle T = 3x - 25, which is a possible value of x?

f. 25
g. 30
h. 35
j. 40

So far I've just drawn a picture for reference and I've been pondering about the problem for about 15 to 20 minutes now. My question is how do I figure out the value of x?

Answer 1

YOu know R+S+T= 180
2x+10+S+3x-25=180
5x+S=195
Now, Angle T<R<S from the opposite sides.

So S is the largest angle, which means that it has to be greater than 60 deg.
S=195-5x
or 195-5x>60
or 135<5x or x<27

Answer 2

25