Two acute angles cannot form a supplementary angles. Justify.
Give a very good explanation please.
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Answered by
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Acute angles, by definition, are angles that measure greater than 0° and less than 90°, or 0°<θ<90°.0°<θ<90°.
Supplementary angles, by definition, are positive angles that add up to 180°.
If you add two acute angles that are each as large as possible, their sum will be less than 180°, so they can’t be supplementary.
If one angle of a supplementary pair is acute, the other must be obtuse to make up the difference.
If one angle of a supplementary pair is a right angle, the other one must also be a right angle, because 90°+90°=180°.
With all that said, three or more angles that are each acute can be supplementary; a simple example would be 60°+60°+60°=180
Supplementary angles, by definition, are positive angles that add up to 180°.
If you add two acute angles that are each as large as possible, their sum will be less than 180°, so they can’t be supplementary.
If one angle of a supplementary pair is acute, the other must be obtuse to make up the difference.
If one angle of a supplementary pair is a right angle, the other one must also be a right angle, because 90°+90°=180°.
With all that said, three or more angles that are each acute can be supplementary; a simple example would be 60°+60°+60°=180
Answered by
28
They cannot. Their sum must be 180 o to be supplementary, but it will be less than 180 o because each acute angle is less than 90 o .
Explanation:
Angles
∠ A and ∠ B are supplementary if their sum measures 180 o .
Acute angle are those measured less than 90o .
If ∠ A < 90 o and ∠ B < 90 o then ∠ A + ∠ B < 180 o
Therefore, two acute angle cannot be supplementary to each other.
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