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 = (7x + 4y)° and m∠2 = (7x + y)°, find x and y.

Answer 1

Answer: The value of x is 10 and the value of if y is 8.

Explanation:

First mark the angles 3, 4 and 5 as shown in below figure.

If a transversal intersects the two f three parallel lines, the corresponding angles are always equal.

From the figure is noticed that the angle 3, 5 and 2 are corresponding angles.

It is given that the angle 3 is 78 degree. So,

$\angle 3=\angle 5=\angle 2=78^{\circ}$

Since the angles 1 and 5 are supplementary angles, therefore there sum is 180 degree.

$\angle 1+\angle 5=180^{\circ}$

$\angle 1+78^{\circ}=180^{\circ}$

$\angle 1=180^{\circ}-78^{\circ}$

$\angle1=102^{\circ}$

It is given that $\angle 1 = (7x + 4y)^{\circ}$ and $\angle 2 = (7x + y)^{\circ}$

$7x+4y=102$        .....(1)

$7x+y=78$            .....(2)

Subtractact equation (2) form equation (1).

$3y=24$

$y=8$

$x=10$

Therefore, the value of x is 10 and the value of if y is 8.