Classify each angle as acute, right, obtuse, or straight. Then find the measures of the complement and the supplement of each angle.
m∠A= 45°m angle eh equals 45 degrees
m∠B= 105°m angle b equals 105 degrees
m∠C= 75°
m angle c equals 75 degrees
Angle A: Acute; Complement: 45°; Supplement: 135°
Angle B: Obtuse; Complement: 75°; Supplement: 105°
Angle C: Acute; Complement: 75°; Supplement: 105°
To classify each angle and find the measures of their complement and supplement, we need to understand the different types of angles:
1. Acute angle: An acute angle is an angle that measures less than 90 degrees.
2. Right angle: A right angle is an angle that measures exactly 90 degrees.
3. Obtuse angle: An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees.
4. Straight angle: A straight angle is an angle that measures exactly 180 degrees.
Now let's classify each angle and find their complement and supplement:
1. Angle A:
- Classification: Since angle A measures 45 degrees, it is an acute angle.
- Complement: The complement of angle A is the angle that, when added to angle A, equals 90 degrees. So, the complement of the acute angle A would be 90 degrees - 45 degrees = 45 degrees.
- Supplement: The supplement of angle A is the angle that, when added to angle A, equals 180 degrees. So, the supplement of the acute angle A would be 180 degrees - 45 degrees = 135 degrees.
2. Angle B:
- Classification: Since angle B measures 105 degrees, it is an obtuse angle.
- Complement: The complement of angle B is the angle that, when added to angle B, equals 90 degrees. Since an obtuse angle does not have a complement within 90 degrees, we cannot find the complement of angle B.
- Supplement: The supplement of angle B is the angle that, when added to angle B, equals 180 degrees. So, the supplement of the obtuse angle B would be 180 degrees - 105 degrees = 75 degrees.
3. Angle C:
- Classification: Since angle C measures 75 degrees, it is an acute angle.
- Complement: The complement of angle C is the angle that, when added to angle C, equals 90 degrees. So, the complement of the acute angle C would be 90 degrees - 75 degrees = 15 degrees.
- Supplement: The supplement of angle C is the angle that, when added to angle C, equals 180 degrees. So, the supplement of the acute angle C would be 180 degrees - 75 degrees = 105 degrees.
So, the classifications, complements, and supplements for the given angles are:
- Angle A: Acute, Complement = 45 degrees, Supplement = 135 degrees
- Angle B: Obtuse, Cannot find complement, Supplement = 75 degrees
- Angle C: Acute, Complement = 15 degrees, Supplement = 105 degrees
To classify each angle as acute, right, obtuse, or straight:
m∠A = 45°
- Acute angle: An angle that measures between 0° and 90°
- Therefore, ∠A is an acute angle.
m∠B = 105°
- Obtuse angle: An angle that measures between 90° and 180°
- Therefore, ∠B is an obtuse angle.
m∠C = 75°
- Acute angle: An angle that measures between 0° and 90°
- Therefore, ∠C is an acute angle.
To find the measures of the complement and the supplement of each angle:
Complement of ∠A:
- the complement of ∠A is the angle that, when added to ∠A, sums up to 90°.
- Complement of ∠A = 90° - 45° = 45°
Supplement of ∠A:
- the supplement of ∠A is the angle that, when added to ∠A, sums up to 180°.
- Supplement of ∠A = 180° - 45° = 135°
Complement of ∠B:
- the complement of ∠B is the angle that, when added to ∠B, sums up to 90°.
- Complement of ∠B = 90° - 105° = -15° (Since an angle cannot be negative, the complement of ∠B is not defined.)
Supplement of ∠B:
- the supplement of ∠B is the angle that, when added to ∠B, sums up to 180°.
- Supplement of ∠B = 180° - 105° = 75°
Complement of ∠C:
- the complement of ∠C is the angle that, when added to ∠C, sums up to 90°.
- Complement of ∠C = 90° - 75° = 15°
Supplement of ∠C:
- the supplement of ∠C is the angle that, when added to ∠C, sums up to 180°.
- Supplement of ∠C = 180° - 75° = 105°