Download Template for Practice Set C L5

Identify angle relationships of parallel lines cut by multiple transversals to form
triangles by using informal arguments about congruent and supplementary
angles, Practice Set C
Name:
Date:
1. Nadia’s friend Janessa came to practice on the
balance beam with her.
a. Use a straight edge or ruler to draw in the three sets of lines that look
parallel. Assume lines that look parallel and perpendicular are.
b. If the angle Nadia makes at the beam with her arm and leg is 43o determine
as many of the rest of the angles as possible. Justify your reasoning for each
angle measure.
2. Use the diagram to answer the questions below.
a. List 8 combinations of 2 of 3 angles that add up to 180 degrees.
Hint: there are at least 16 sets of angle combinations that add up to 180
degrees!
b. Let angle 6 equal 153 degrees and angle 7 equal 83 degrees. Determine the
measures of the remaining angles and justify your reasoning for each.
Identify angle relationships of parallel lines cut by multiple transversals to form
triangles by using informal arguments about congruent and supplementary
angles, Practice Set C Answer Key
1. Nadia’s friend
Janessa came to practice
on the balance beam
with her.
a. Use a straight edge or ruler to draw in the three sets of lines that look
parallel. Assume lines that look parallel and perpendicular are.
b. If the angle Nadia makes at the beam with her arm and leg is 43o determine
as many of the rest of the angles as possible. Justify your reasoning for each
angle measure.
Assuming that lines that look perpendicular are, then angles a, b, c, d, e, j, k,
p, and s are all right angles.
Therefore, the measure of angle f is 47 degrees either by triangle angle sum or
exterior and remote interior relationships.
The measure of angle g is 47 degrees because it is alternate interior to f.
The measure of angle h is 133 degrees because it is supplementary or a linear
pair with f.
The measure of angle i is 133 degrees because it is alternate interior to h or
same side interior to g.
The measure of angle m is 47 degrees because it’s same side interior to angle
i. The measure of angle n is 43 degrees either by triangle angle sum or
exterior and remote interior relationships.
The measure of angle t is 137 degrees either by being supplementary or a
linear pair with angle n or by exterior and remote interior angle relationships.
2. Use the diagram to answer
the questions below.
a. List 8 combinations of 2 of 3 angles that add up to 180 degrees.
Hint: there are at least 16 sets of angle combinations that add up to 180
degrees!
1 and 2- supplementary/linear pair
1 and 3- supplementary/linear pair
3 and 4- supplementary/linear pair
2 and 4- supplementary/linear pair
10 and 11- supplementary/linear pair 7 and 11- supplementary/linear pair
7, 8 and 9- supplementary
8, 9 and 10- supplementary
5 and 6- supplementary/linear pair
6 and 9- same side interior
5, 7 and 8- same side interior
1 and 7- same side interior
2, 8 and 9- same side interior
3 and 11- same side exterior
4 and 10- same side exterior
2, 5 and 8- triangle angle sum
4 and 7- substitution
3, 8 and 9- substitution
2 and 11- substitution
1 and 10- substitution
b. Let angle 6 equal 153 degrees and angle 7 equal 83 degrees. Determine the
measures of the remaining angles and justify your reasoning for each.
The measure of angle 1 is 97 degrees by same side interior to angle 6.
The measure of angle 2 is 83 degrees by supplementary to angle 1.
The measures of angles 3 and 4 are 83 degrees and 97 degrees respectively by
being vertical to angles 2 and 1.
The measure of angle 5 is 27 degrees because it is supplementary to angle 6.
The measure of angle 8 is 70 degrees by triangle angle sum.
The measure of angle 9 is 27 degrees because it is alternate interior to angle 5.
The measure of angle 10 is 83 degrees because it is vertical to angle 7.
The measure of angle 11 is 97 because it is corresponding to angle 1.
Justifications may vary, as other valid reasoning exists.