Question

The figure below shows a pair of lines crossed by a transversal. All of the angles are labeled with numbers. Using the numbers, give one pair of each of the types of angles listed below.

Answer 1

a. Vertical angles: 1 and 4, 2 and 3, 5 and 8, 6 and 7.

b. Supplementary angles: 1 and 2, 2 and 4, 3 and 4, 1 and 3, 5 and 6,

6 and 8, 7 and 8, 5 and 7.

c. Corresponding angles: 1 and 5, 2 and 6, 3 and 7, 4 and 8.

d. Alternate interior angles: 3 and 6, 4 and 5.

e. Alternate exterior angles: 1 and 8, 2 and 7.

Explanation:

a. Vertical angles (opposite by the vertex):

1 and 4, 2 and 3, 5 and 8, 6 and 7

b. Supplementary angles (sum 180°):

1 and 2, 2 and 4, 3 and 4, 1 and 3, 5 and 6, 6 and 8, 7 and 8, 5 and 7

c. Corresponding angles (same position respect the right lines and the secant):

1 and 5, 2 and 6, 3 and 7, 4 and 8

d. Alternate interior angles (between the lines but in different position with respect the secant):

3 and 6, 4 and 5

e. Alternate exterior angles (not between the lines and in different position with respect the secant):

1 and 8, 2 and 7