Question

select the correct answer. prove: if two angles are supplementary, then one of the angles must be obtuse. which image provides a counterexample to this statement? a. image of angle with right angle b. image of angle with acute and obtuse c. image of two angles d. image of two angles

Explanation:

1. Supplementary angles sum to $180^\circ$.
2. An obtuse angle is greater than $90^\circ$ and less than $180^\circ$.
3. In option A, $\angle AMB = 90^\circ$ and $\angle CMB = 90^\circ$. Their sum is $90^\circ + 90^\circ = 180^\circ$, so they are supplementary.
4. Neither angle is obtuse (they are right angles), which directly contradicts the statement that one angle must be obtuse. This makes it a valid counterexample.

Answer:

A. (The diagram with two right angles at point M: ∠AMB and ∠CMB, each 90°)