Question

Ocean waves move in parallel lines toward the shore. The figure shows Sandy Beaches windsurfing across several waves. For this problem, think of Sandy’s wake as a line. m∠1 = (2x + 10)° and m∠2 = (4y − 30)°. 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°

Answer 2

Angle 2 is the same as the given angle of 70 degrees so we can solve for y:

4y-30 = 70

Add 30 to both sides:

4y = 100

Divide both sides by 4:

Y = 25

Angle 1 and angle two are supplementary angles and when added together need to equal 180:

We know angle 2 = 70, so angle 1 must equal 180-70 = 110

2x + 10 = 110

Subtract 10 from both sides:

2x = 100

Divide both sides by 2:

X = 50

The answer is:

X = 50, y = 25