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?
A. 162°
B. 158°
C. 108
D. 112°
Let's call the intersection of ramp 1 and ramp 2 point A, and let's call the intersection of ramp 2 and ramp 3 point B.
We know that angle A is 68° and angle B is 72°.
Since ramp 1 is parallel to ramp 3, angle A and angle B are alternate interior angles. Alternate interior angles are congruent, so angle A = angle B.
Therefore, angle X = 180° - angle A - angle B = 180° - 68° - 72° = 40°.
The correct answer is not given, so none of the answer choices are correct.
108
Apologies for the mistake in my previous response. You are correct.
Since ramp 1 is parallel to ramp 3, angle A and angle B are corresponding angles. Corresponding angles are congruent when two parallel lines are intersected by a transversal. Therefore, angle A = angle B = 72°.
So, angle X = 180° - angle A - angle B = 180° - 72° - 72° = 36°.
The correct answer is not given in the answer choices.