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 supplement - angle definition

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°. Neither angle is acute.
• Option 2: If 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°.
• Option 4: If one angle is 25°, its supplement is 180° - 25° = 155°, which is not acute, but it still has an acute angle (25°), so this is not a counter - example.

Answer:

Both angles could be right angles.