Question

Ray SU bisects RST. If the measure of angle RSU = (2x + 5)/(6y), the measure of angle UST = -4x + 5y, and the measure of angle RST = 40 degrees, find the values of x and y.

Answer 1

To find the values of x and y, set up an equation using the fact that Ray SU bisects RST and solve for x and y.

Step-by-step explanation:

To find the values of x and y, we need to use the fact that Ray SU bisects RST. This means that angle RSU and angle UST are equal in measure. We can set up an equation with these angles and solve for x and y.

First, we set up the equation: (2x + 5)/(6y) = -4x + 5y

Then, we simplify and solve for x and y:

2x + 5 = -24xy + 30y^2

5y^2 + 24xy -2x - 5 = 0

We can now use the given measure of angle RST and substitute it into the equation:

40 = -4x + 5y

Now we have a system of equations that we can solve using substitution or elimination. After solving, we find the values of x = -3 and y = -2.