What is measure of an angle R?

Question

side SR is unknown,ST is (12x-15)degree and TR is (3x+30) degree.
answer choice A: 45 degree
B: 52.5 degree
C: 63 degree
D: 75 degree
please help and explain step by step. Thank you in advance.

Answer 1

ST is (12x-15)degree and TR is (3x+30) degree

That does not make sense. Please check for typos. ST and TR are LENGTHS, not angles in degrees.

if they are angles we need to know some length
if they are lengths, we need to know an angle.

Answer 2

thank you so much for answering my inequality question.
ok here is the link for this question. Question number 14.

studylib.net/doc/8749401/geometry-b-final-exam-multiple-choice-practice-problems

Answer 3

I agree with Damon, what you described does not match the question in your link
angles are identified by 3 letters, with the middle letter referring to the vertex of the angle
e.g. you should have said
angle TSR = (12x - 15)° , etc

You also failed to mention, that the triangle is isosceles, which happens to be the critical
part of the question
so angle SRT = angle STR = (3x + 30)°

so we have 3x+30 + 3x+30 + 12x-15 = 180
18x = 135
x = 135/18 = 15/2 °

so angle R = 3x + 30 = 45/2 + 30 = 52.5

angle R = 52.5°

check: 52.5+52.5+12(15/2)-15 = 180, ok