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.
Accepted Solution
A:
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°