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: Both angles could be right angles

If both angles are right angles (90° each), their sum is 90°+90° = 180°, and neither is acute. This is a valid counter - example.

Option 2: When one angle is 135°, the supplement is 180° - 135°=45°, which is acute. This does not disprove the conjecture.

Option 3: Both angles cannot be straight angles because 180°+180° = 360°≠180°, so they are not supplementary.

Option 4: When one angle is 25°, the supplement is 180° - 25° = 155°, which is not acute, but this does not disprove the "one of the angles must be acute" part of the conjecture as it still has an acute angle (25°).

Answer:

Both angles could be right angles.