angle R and angle S are complementary which means they add to 90 degrees. Think "C" for "Complementary" and "Corner" as in a sharp 90 degree corner. That's how I remember it.
Angle 1 and angle 2 "form a linear pair". This means they are adjacent and supplementary (add to 180 degrees). Put another way, they combine to form a single straight angle or line.
Let's make x = measure of angle 1 y = measure of angle 2
We're also told that "the measure of angle 2 is six more than twice the measure of angle 1", which basically translates to y = 2*x + 6
Because the angles (x and y) are supplementary, we can also say x+y = 180
So we have this system of equations y = 2x+6 x+y = 180
Start with equation (2). Plug in the equation (1) and solve for x x+y = 180 x+2x+6 = 180 ... note how y has been replaced with 2x+6 3x+6 = 180 3x+6-6 = 180-6 3x = 174 3x/3 = 174/3 x = 58
Now that we know x, we can find y y = 2x+6 y = 2*58+6 y = 116+6 y = 122
