UNIT 4 QUIZ STUDY GUIDE: Angles & Relationship

Complementary angles

• are congruent

• sum up to 90 degrees

• sum up to 180 degrees

• sum up to 360 degrees

Answer explanation

Complementary angles are defined as two angles whose measures sum up to 90 degrees. Therefore, the correct choice is that complementary angles sum up to 90 degrees.

Supplementary angles

• are congruent

• sum up to 90 degrees

• sum up to 180 degrees

• sum up to 360 degrees

Answer explanation

Supplementary angles are defined as two angles whose measures add up to 180 degrees. Therefore, the correct choice is that supplementary angles sum up to 180 degrees.

The measures of vertical angles:

• always add up to 180.

• are always congruent.

• always add up to 90.

Answer explanation

Vertical angles are formed by two intersecting lines and are always congruent, meaning they have equal measures. Therefore, the correct answer is that the measures of vertical angles are always congruent.

_________ is the sum of two or more angles equals 180 degrees.

• Complementary angle

• Vertical angle

• Supplementary angle

• None

Answer explanation

Supplementary angles are defined as two angles whose sum is 180 degrees. In contrast, complementary angles sum to 90 degrees, and vertical angles are equal but not defined by a sum. Thus, the correct answer is 'Supplementary angle'.

_________ is the sum of two or more angles equals 90 degrees.

• Complementary angle

• Vertical angle

• Supplementary angle

• None

Answer explanation

Complementary angles are defined as two angles whose sum is 90 degrees. This distinguishes them from supplementary angles, which sum to 180 degrees, and vertical angles, which are equal but not defined by a specific sum.

∠ABD and ∠CBD are supplementary angles. Find the value of x.

• 15 degrees

• 90 degrees

• 45 degrees

• 75 degrees

Find the complementary angle of a 18° angle.

• 162°

• 45°

• 72°

• 60°

Answer explanation

The complementary angle of an angle is found by subtracting it from 90°. For an 18° angle, the calculation is 90° - 18° = 72°. Therefore, the complementary angle is 72°.

Find the complementary angle of a 58° angle.

• 122°

• 32°

• 180°

• 90°

Answer explanation

The complementary angle of an angle is found by subtracting it from 90°. Therefore, 90° - 58° = 32°. Thus, the complementary angle of a 58° angle is 32°.

Find the supplementary angle of a 18° angle.

• 162°

• 72°

• 180°

• 90°

Answer explanation

The supplementary angle is found by subtracting the given angle from 180°. Thus, 180° - 18° = 162°. Therefore, the supplementary angle of an 18° angle is 162°.

Find the supplementary angle of a 45° angle.

• 155°

• 135°

• 55°

• 45°

Answer explanation

The supplementary angle is found by subtracting the given angle from 180°. For a 45° angle, 180° - 45° = 135°. Therefore, the supplementary angle is 135°.