Question 1116536: a. Using geometry terms, identify what the side road would be called?
b. Identify the vertical angles, linear pair angles, and supplementary angles and explain your reasoning.
c. A fourth road is going to be constructed. Is there a way it could be placed to create complementary angles? Explain.
picture:https://api.agilixbuzz.com/Resz/~zd4LEAAAAAgaibrmLN2XTA.ME7Kp727ci0kvJzF5hKYcC/48780742,5BB,0,0/Assets/Media/Images/41.1-HOT3-Highway.jpg
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! this looks like 2 parallel lines cut by a transversal.
consider the roads to be very fat lines.
the main road is the transversal.
the two side roads are parallel to each other.
vertical angles would be:
1 and 4
2 and 3
5 and 8
6 and 7
linear pairs would be:
1 and 3
2 and 4
5 and 7
6 and 8
1 and 2
3 and 4
5 and 6
7 and 8
supplementary angles would be:
3 and 5
4 and 6
these are in additional to the linear pairs which are also supplementary.
congruent angles would be:
1 and 5
3 and 7
2 and 6
4 and 8
these are in additional to the vertical angles which are also congruent.
all the angles formed by parallel lines are either congruent or supplementary.
here's a reference on parallel lines.
https://www.varsitytutors.com/hotmath/hotmath_help/topics/transversal
to create complementary angles, you need to make a road that is cut in such a way that the angles formed can be summed up to be 90 degrees.
90 degrees angles are made by roads that are perpendicular to each other.
if you make a fourth road that is perpendicular to the main road, or perpendicular to the two side roads, it will form right triangle.
the acute angles of the triangles will be complementary because their sum will be 90 degrees.
here's my diagram or your roads, followed by a diagram of your roads shown as solid lines.
both diagrams shows the fourth road perpendicular to the two side roads which are parallel to each other.
the triangle formed is a right triangle with one 90 degree angle and the other two angles of the triangle being complementary to each other.
sum of the angles of a triangle is 180 degrees.
right angle is 90.
that leave 90 for the other two angles, making them complementary to each other.
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