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 40° angle. What are the values of x and y?
A picture of a miniature golf course is shown. The path of the ball goes to a wall and bounces off the wall. A dashed line is drawn to the wall and the angle between the wall and the dashed line is marked as a right angle. The angle formed by the path of the ball to the wall and the dashed line is labeled 40 degrees. The angle between the path of the ball to the wall and the wall is labeled x degrees. The angle between the path of the ball away from the wall and the wall is labeled y degrees.
The image shows the path of a ball beginning on the upper left, hitting the wall and bouncing off toward the upper right of the diagram.
A dashed line segment is drawn vertically from the top center edge of the diagram to the wall. The intersection is marked with a small square.
A white line segment is drawn from the ball to this point of intersection.
The angle between the white line segment and the wall is labeled x degrees.
The angle between the white line segment and the dashed vertical line segment is labeled 40 degrees.
A second white line segment extends from the point of intersection of the dashed vertical line segment with the wall to the hole at the upper right.
The angle formed by the wall and this line segment is labeled y degrees.
(1 point)
Responses
x = 50; y = 40
x = 50; y = 40
x = 40; y = 50
x = 40; y = 50
x = 50; y = 50
x = 50; y = 50
x = 40; y = 40
In the given diagram, the ball hits the wall at a 40 degree angle. The value of x, which represents the angle between the path of the ball towards the wall and the wall itself, can be found by subtracting 40 from 90 (as it forms a right angle with the dashed line). Therefore, x = 90 - 40 = 50 degrees.
Similarly, the value of y, which represents the angle between the path of the ball away from the wall and the wall, can be found by subtracting x from 90 (as it forms a right angle with the dashed line). Therefore, y = 90 - x = 90 - 50 = 40 degrees.
So, the values of x and y are x = 50 and y = 40.