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
Here is link for this question number 14. Thanks in advance.
studylib.net/doc/8749401/geometry-b-final-exam-multiple-choice-practice-problems
you cannot specify an angle by using two points. Either name all three points, or just name the vertex. You should have said
angle S = (12x-15)degrees and T is (3x+30) degrees
So, since SR ≅ ST, ∡R ≅ ∡T
So, since the sum of the angles of a triangle is 180 degrees, we have
(12x-15) + 2(3x+30) = 180
Solve for x, and then you can find R.
Just answered this:
https://www.jiskha.com/questions/1827652/what-is-measure-of-an-angle-r-side-sr-is-unknown-st-is-12x-15-degree-and-tr-is-3x-30
To find the measure of angle R, we can use the fact that the angles in a triangle add up to 180 degrees.
In this case, we have a triangle STR. The known angles are ST = (12x-15) degrees and TR = (3x+30) degrees. The measure of angle R is what we're trying to find.
To find the measure of angle R, we can set up an equation:
ST + TR + angle R = 180 degrees
Substituting the known values:
(12x-15) + (3x+30) + angle R = 180
Combining like terms:
15x + 15 + angle R = 180
Simplifying:
15x + angle R = 165
Now we need to solve for x in order to find the value of angle R. Unfortunately, without the other side lengths of the triangle (SR and ST), we won't be able to find the exact value of x and therefore the exact measure of angle R.
However, we can check each of the answer choices given and see if any of them would allow us to find a valid value of x that satisfies the equation we set up.
Let's check each answer choice:
A: 45 degrees
15x + 45 = 165
This equation does not have a valid solution for x since it leads to a contradiction.
B: 52.5 degrees
15x + 52.5 = 165
This equation does not have a valid solution for x either.
C: 63 degrees
15x + 63 = 165
This equation does have a valid solution for x:
15x = 102
x = 6.8
D: 75 degrees
15x + 75 = 165
This equation does not have a valid solution for x as well.
Therefore, among the answer choices provided, the only option that leads to a valid solution is C: 63 degrees.
So, the measure of angle R is 63 degrees.