Question

Ocean waves move in parallel lines toward the shore. The figure shows the path that a windsurfer takes across several waves. For this exercise, think of the windsurfer's wake as a line. If m∠1 = (5x + 3y)° and m∠2 = (5x + y)°, find x and y.

Answer 1

If you look at the figure, the angle marked red is equal to 70° because vertical angles are equal. So, that also means that the opposite angle 2 is also 70°. So, the first equation is:

70 = 5x + y

Next, the green angle as marked is equal to
Green angle = 180 - 70 = 110
Being vertical angles, angle 1 is then equal to 110°. So,the second equation is

110 = 5x + 3y

Subtract the two equations:

    5x + y = 70
 -  5x + 3y = 110
________________
           -3y = -40
              y = -40/-3 = 13.33°

Substituting y to either one of the equations,
5x + 13.33 = 70
Solving for x,
x = 11.33°