angles across each other at a junction, namely vertical angles, are equal.
so the angles right in the middle, where both triangles intersect, are both equal, that means the triangles have that angle in common as well as the angle x°, meaning both triangles are similar by AA.
if both triangles are similar, that means all their interior angles are the same, meaning y = 75°.
now, let's notice something, those tickmarks, meaning each triangle is an isosceles triangle, which have a vertex angle and twin angles.
since all interior angles in a triangle add up to 180°, so 180 - 75 = 105°, subtracting "y" from the 180°, that leaves 105°, to be split evenly between the twin angles of "x" and the one at the junction.
105/2 = 52.5° = x.
Answer:
1.4 hour, or 1 hr 24 min
Step-by-step explanation:
The trains separate at the rate (80 + 90) mph.
Recall that distance = rate times time, or time = distance / rate.
238 mi
Here, the elapsed time is -------------- = 1.4 hr, or 1 hr 24 min
170 mph
