What is the measurement of theta in degrees?

Hello from MrBillDoesMath!

 48.2 degrees

Discussion:

In the diagram, "6" is the x- distance along the side adjacent to theta, and  

3 * sqrt(5) is the y-distance along the side opposite angle theta.

By definition of tangent of angle, using "@" for theta, we have

tan (@)        =  opposite/adjacent = 3 * sqrt(5) / 6  = sqrt(5)/2

So @ = (inverse tangent (sqrt(5)/2) )  =  48.189 degrees (approximately)

Thank you,

MrB

5x - 6y = -90

-10 x - 6y = -90

Subtracting,

15x = 0

x = 0

y = -90/(-6) = 15

x=0, y=15