Question

If m RST=65, m QST=2x, and m QSR= 3x-10, what is the value of x?

Answer 1

Upon drawing the triangles given, it may be observed that they share one common side, ST. Hence, m QSR is the sum of m RST and m QST. Mathematically,
3x - 10 = 65 + 2x
The value of x from the equation generated above is 75. Thus, the answer to the question above is 75.

Answer 2

First, draw a quadrilateral figure QRST. Then, label angles RST, QST, and QSR.

Given:

mRST = 65
mQST = 2x
mQSR = 3x - 10

From the figure, angle RST is the sum of angles QST and QSR. Therefore:

mRST = mQST + mQSR

Substituting the values, the equation becomes:

65 = 2x + (3x -10)

Solve for x:

x = 15