What is measure of an angle R?
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.
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
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.
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
To find the measure of angle R, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Step 1: Start by setting up an equation using the given angles:
(12x - 15) + (3x + 30) + R = 180
Step 2: Simplify the equation by combining like terms:
15x + 30 + R = 180
Step 3: Subtract 30 from both sides to isolate the variable:
15x + R = 150
Step 4: Subtract 15x from both sides to isolate the variable:
R = 150 - 15x
Step 5: We do not have enough information to solve for the exact value of R. However, we can check which answer choice could be the measure of angle R by substituting the values of x given in each answer choice.
Let's go through the answer choices one by one:
A: If R = 45 degrees, then the equation becomes:
45 = 150 - 15x
15x = 105
x = 7
By substituting x = 7 into the given angles, we find that (12x - 15) = 69 degrees and (3x + 30) = 51 degrees. Adding up the three angles, we get 120 degrees, not 180 degrees. Therefore, A is not the correct answer.
B: If R = 52.5 degrees, then the equation becomes:
52.5 = 150 - 15x
15x = 97.5
x = 6.5
By substituting x = 6.5 into the given angles, we find that (12x - 15) = 69 degrees and (3x + 30) = 51.5 degrees. Adding up the three angles, we get 172 degrees, not 180 degrees. Therefore, B is not the correct answer.
C: If R = 63 degrees, then the equation becomes:
63 = 150 - 15x
15x = 87
x = 5.8
By substituting x = 5.8 into the given angles, we find that (12x - 15) = 63.6 degrees and (3x + 30) = 47.4 degrees. Adding up the three angles, we get 180 degrees. Therefore, C is the correct answer.
D: If R = 75 degrees, then the equation becomes:
75 = 150 - 15x
15x = 75
x = 5
By substituting x = 5 into the given angles, we find that (12x - 15) = 65 degrees and (3x + 30) = 45 degrees. Adding up the three angles, we get 185 degrees, not 180 degrees. Therefore, D is not the correct answer.
Thus, the measure of angle R is 63 degrees, corresponding to answer choice C.