Which of the following statements is true?
1) Two acute angles can be complementary to each other.
2) Two obtuse angles can be complementary to each other.
3) Two right angles can be complementary to each other.
4) one obtuse angle and one acute angle can be complementary to each
other.
Answers
Answer:
1) Two acute angles can be complementary to each other.
Explanation in Words:
An acute angle is an angle which is less than 90°. An obtuse angle is an angle which is greater than 90°, but less than 180°.
Complementary means two angles of which the sum is 90°.
Obviously, the sum of two numbers greater than 90° cannot be 90°. It is always over 180°.
For example, the sum of 91° and 98°, which is 189°. 189° is greater than 90°. 189° is a reflex angle, which means that it is greater than 180°.
The sum of two right angles (90°) is always 180°.
The sum of an obtuse angle and an acute angle is a reflex angle, a straight angle (180°) or an obtuse angle.
For example, the sum of 91° and 43° is 134°, which is an obtuse angle. Another example is, the sum of 178° and 3°, which is 181°. That is a reflex angle. The sum of 175° and 5° is 180°.
Explanation in Numbers:
1. a) Acute Angle < 90°
2. a) Obtuse Angle > 90°
2. b) Obtuse angle < 180°
3. a) Right Angle = 90°
4. a) Reflex Angle > 180°
4. b) Reflex Angle < 360°
5. a) Straight Angle = 180°
6. a) Complete Angle = 360°
Remarks:
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Answer:
3
Step-by-step explanation:
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