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. both angles could be right angles. when one angle is 135°, the supplement is not acute. both angles could be straight angles. when one angle is 25°, the supplement is not acute.

Explanation:

Step1: Recall angle - supplement and type definitions

Two angles are supplementary if their sum is 180°. An acute angle is an angle with a measure between 0° and 90°, a right - angle has a measure of 90°, and a straight - angle has a measure of 180°.

Step2: Analyze each option

• Option 1: If both angles are right angles (90° each), 90°+90° = 180°, and neither is acute. This is a valid counter - example.
• Option 2: When one angle is 135°, its supplement is 180° - 135°=45°, which is acute, so this is not a counter - example.
• Option 3: Two straight angles (180° each) cannot be supplementary since 180°+180°=360°≠180°, so this is not a valid option.
• Option 4: When one angle is 25°, its supplement is 180° - 25° = 155°, which is not acute, but it doesn't disprove the conjecture as strongly as two right angles. The conjecture says "one of the angles must be acute", and two right angles show that neither has to be acute.

Answer:

Both angles could be right angles.