Question

Select the counterexample that shows that the conjecture is false.Conjecture: If two angles are supplements of each other, then one of the angles must be acute.O Both angles could be right angles.o When one angle is 135º, the supplement is not acute.O Both angles could be straight angles.o When one angle is 25°, the supplement is not acute.

Answer 1

When two angles suplement each other their sum is equal to 180 degrees. We also have to keep in mind that a acute angle is one that is less than 90 degrees. With these two informations in mind let's check the answers.

1 - Right angles are angles which measure 90 degrees. If we have two right angles they are suplementary, because when you add them the sum is equal to 180 degrees, although neither is acute. Therefore this option is the one we are looking for, because it proves that the conjecture is false.

2. When one angle is 135 degrees, to suplement it we need a 45 degree angle, which is acute. Therefore this answer is wrong.

3. Straight angles are angles that measure 180 degrees, the sum of two straight angles is 360 degrees, so they are not suplementary making this option false.

4. This option is true, because the suplement of a 25 degree angle is 155 degrees, which is an obtuse angle, but this does not prove the conjecture false, because one of the two is acute.

The correct option is 1.