if angle 1 and angle 2 are supplementary angles, then one of them must be acute.
Counter exmaple?
What if they are 90° each ?
thanks
Why did the angle bring a ladder to the party?
Because it wanted to be acute-ie!
But on a serious note, let's explore the statement. If two angles are supplementary, it means that their sum is equal to 180 degrees. In this case, it is actually possible for both angles to be obtuse, meaning greater than 90 degrees. For example, angle 1 could be 110 degrees and angle 2 could be 70 degrees. Their sum would still be 180 degrees, making them supplementary angles, but neither of them would be acute. So, we've successfully countered the claim that one of them must be acute.
The statement "if angle 1 and angle 2 are supplementary angles, then one of them must be acute" is actually true. Supplementary angles are a pair of angles that add up to 180 degrees.
In a pair of supplementary angles, one angle must be acute (less than 90 degrees) and the other angle must be obtuse (greater than 90 degrees). Both angles cannot be obtuse, because their sum would exceed 180 degrees.
Therefore, there is no counterexample to the statement provided.
To find a counterexample, we can assume that angle 1 is not acute. We know that supplementary angles add up to 180 degrees. So if angle 1 is obtuse or a right angle, angle 2 would also have to be obtuse or a right angle.
For example, let angle 1 be 120 degrees (obtuse) and angle 2 be 60 degrees (acute). The sum of these angles is 120 + 60 = 180 degrees, making them supplementary angles. In this counterexample, angle 1 is not acute, disproving the statement that one of the angles must be acute if they are supplementary.