A child's toy consists of two parallel posts supporting three ramps for rolling a wooden car. Ramp 1 is parallel to ramp 3.
Picture not drawn to scale.
The angle formed by ramp 1 and the left post is 72°, while the angle formed by ramp 2 and the left post is 68°. What is the measure of angle X?
To find the measure of angle X, we first need to analyze the given information.
We know that ramp 1 is parallel to ramp 3. Therefore, the angle formed by ramp 1 and the right post is also 72°.
Similarly, since ramp 2 is parallel to ramp 3, the angle formed by ramp 2 and the right post is 68°.
Now, let's focus on the angle formed by ramp 1 and ramp 2, which is the angle X.
Since ramp 1 is parallel to ramp 3, the angle formed by ramp 1 and ramp 2 is equal to the angle formed by ramp 3 and ramp 2.
Let's call this angle A.
So, we have:
Angle A + 68° + 72° = 180° (because the sum of angles in a triangle is 180°)
Angle A + 140° = 180°
Angle A = 180° - 140° = 40°
Therefore, the measure of angle X is 40°.