Question

in the game of miniature golf, the ball bounces off the wall at the same angle it hit the wall. (this is the angle formed by the path of the ball and the line perpendicular to the wall at the point of contact) in the diagram, the ball hits the wall at a 34° angle. use the equal complements theorem. what are the values of x and y? x = ° y = °

Explanation:

Step1: Recall angle - wall relationship

The sum of the angle between the ball's path and the perpendicular to the wall and the angle between the ball's path and the wall is 90°.

Step2: Calculate x

Since the angle between the ball's path and the perpendicular to the wall is 34°, and x is the angle between the ball's path and the wall, we know that x + 34°=90°. Solving for x, we get x = 90° - 34°=56°.

Step3: Calculate y

Because the ball bounces off the wall at the same angle it hits the wall (with respect to the perpendicular to the wall), the angle situation on the other side is symmetric. So y also satisfies y+34° = 90°, and y = 90° - 34°=56°.

Answer:

x = 56°, y = 56°