The measures of the angles of triangle ABC add up to 180 degrees:
(x15) + (x/2 +y) + (y+15) = 180
(x + x/2) + (y + y) + (15 + 15) = 180 Like terms grouped together
3x/2 + 2y = 180
We also know that ∠DAB = x + (x  15) + (x/2 + y) and that ∠DAB is a straight angle, so:
x + (x  15) + (x/2 + y) = 180
5x/2 + y 15 = 180
5x/2 + y = 195
We now have a system of equations we can use to solve for x and y:
5x/2 + y = 195
3x/2 + 2y = 180
There are multiple ways to solve a system of equations; I chose to multiply the top equation by 2 and use elimination:
5x  2y = 390
3x/2 + 2y = 180
7x/2 = 210
Multiply both sides by 2/7 and we get:
x = 60
You can plug that in to the equation of your choice and find that y = 45.
Just to check, we can find that the angles of the triangle are 45, 75 and 60, which add to 180.
11/17/2012

Kathye P.