Question

use the figure below to answer #34 - #40.

1. name an angle congruent to ∠5.
2. name an angle complementary to ∠5.
3. name an angle supplementary to ∠5.
4. name an angle adjacent to ∠2.
5. name an angle that forms a linear pair with ∠2.
6. name an angle that forms a pair of vertical angles with ∠2.
7. name an angle that is not adjacent to ∠2.

Explanation:

Step1: Recall angle - relationship definitions

Adjacent angles share a common side and a common vertex. Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. Vertical angles are opposite each other when two lines intersect. Congruent angles have the same measure.

Step2: Analyze each sub - question

34)

Congruent angles have equal measure. If we assume the figure has some equal - measure angles, and we want an angle congruent to ∠5. If the figure has vertical angles or corresponding angles (depending on the nature of the intersecting lines), we look for an angle with the same measure. Let's assume the figure has vertical angles formed by two intersecting lines. If ∠5 and another angle are vertical angles, they are congruent.

35)

Complementary angles add up to 90 degrees. We look for an angle such that when added to ∠5, the sum is 90 degrees. If there is a right - angle formed in the figure and ∠5 is part of it, the other non - right angle adjacent to ∠5 in the right - angle is its complementary angle.

36)

Supplementary angles add up to 180 degrees. We look for an angle such that when added to ∠5, the sum is 180 degrees. If there is a straight line and ∠5 is one of the angles on the straight line, the angle adjacent to it on the straight line is its supplementary angle.

37)

Adjacent angles to ∠2 share a common side and a common vertex with ∠2. We identify the angles that meet these criteria in the figure.

38)

A linear pair is a pair of adjacent angles that form a straight line (sum to 180 degrees). We look for an angle that, along with ∠2, forms a straight line.

39)

Vertical angles are opposite each other when two lines intersect. We look for an angle that forms a pair of vertical angles with ∠2.

40)

We look for an angle that does not share a common side and a common vertex with ∠2.

Answer:

1. Without seeing the figure, assume if there are vertical angles, an angle vertical to ∠5 is congruent to it.
2. Without seeing the figure, if there is a right - angle involving ∠5, the non - ∠5 part of the right - angle is complementary to ∠5.
3. Without seeing the figure, if there is a straight line involving ∠5, the adjacent angle on the straight line is supplementary to ∠5.
4. Identify angles sharing a common side and vertex with ∠2 in the figure.
5. Identify an angle that, with ∠2, forms a straight line in the figure.
6. Identify an angle opposite to ∠2 when two lines intersect in the figure.
7. Identify an angle that does not share a common side and vertex with ∠2 in the figure.