Question

section 2.1 complementary and supplementary angles
complementary angles → two that have a sum of
supplementary angles → two angles that have a of
example 1) determine whether the angles are complementary, supplementary, or neither.
a) b) c)
adjacent angles → two angles are if they share a vertex and
example 2) tell whether the numbered angles are adjacent or nonadjacent.
a) b) c)

Explanation:

Step1: Define complementary angles

Complementary angles are two angles that have a sum of 90°.

Step2: Define supplementary angles

Supplementary angles are two angles that have a sum of 180°.

Step3: Analyze Example 1 - a

The sum of 22° and 158° is 22° + 158°=180°, so they are supplementary.

Step4: Analyze Example 1 - b

The sum of 15° and 85° is 15°+ 85° = 100°, so they are neither complementary nor supplementary.

Step5: Analyze Example 1 - c

The sum of 55° and 35° is 55°+35° = 90°, so they are complementary.

Step6: Define adjacent angles

Two angles are adjacent if they share a common vertex and a common side.

Step7: Analyze Example 2 - a

The angles do not share a common side, so they are non - adjacent.

Step8: Analyze Example 2 - b

The angles share a common vertex and a common side, so they are adjacent.

Step9: Analyze Example 2 - c

The angles share a common vertex and a common side, so they are adjacent.

Answer:

Complementary angles: two angles that have a sum of 90°.
Supplementary angles: two angles that have a sum of 180°.
Example 1:
a) Supplementary
b) Neither
c) Complementary
Adjacent angles: two angles are adjacent if they share a common vertex and a common side.
Example 2:
a) Non - adjacent
b) Adjacent
c) Adjacent