TRUE OR FALSE OR SOMETIMES: When angles form a linear pair, one of the angles is acute.
TRUE OR FALSE OR SOMETIMES: If you know the supplement of an angle you can find its complement.
SOMETIMES (what if they are both 90?)
SOMETIMES (what if the supplement is less than 90?)
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TRUE OR FALSE OR SOMETIMES: When angles form a linear pair, one of the angles is acute.
FALSE. When angles form a linear pair, which means they are adjacent and their non-common sides form a straight line, one angle is always acute and the other angle is always obtuse. An acute angle is an angle that measures less than 90 degrees, while an obtuse angle measures more than 90 degrees.
To understand why this statement is false, we can refer to the definition of a linear pair. A linear pair consists of two adjacent angles whose measures sum up to 180 degrees. Since the sum of two acute angles is always less than 180 degrees, one of the angles in a linear pair must be acute, and the other must be obtuse.
Therefore, it is incorrect to say that when angles form a linear pair, one of the angles is acute. In reality, one angle is always acute, and the other is always obtuse.
TRUE OR FALSE OR SOMETIMES: If you know the supplement of an angle, you can find its complement.
SOMETIMES. The supplement of an angle is another angle that, when added to the original angle, gives a sum of 180 degrees. The complement of an angle is another angle that, when added to the original angle, gives a sum of 90 degrees.
If we have an angle and we know its supplement, we can calculate its complement under certain conditions. Since the supplement and the complement of an angle are related by the equation:
Supplement + Complement = 180 degrees
We can rearrange this equation to solve for the complement:
Complement = 180 degrees - Supplement
So, if we are given the supplement of an angle, we can subtract it from 180 degrees to find the complement. However, it's important to note that this only works if the given angle and its supplement are adjacent angles, as they should be in order to form a linear pair. If the angles are not adjacent or do not form a linear pair, we cannot use the supplement to find the complement.
Therefore, it is sometimes true that if you know the supplement of an angle, you can find its complement, but only when the given angle and its supplement are adjacent angles forming a linear pair.