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.
○ b.
○ c.
○ d.

Explanation:

A counter - example to the statement "If two angles are supplementary, then one of the angles must be obtuse" is a case where two angles are supplementary but neither is obtuse.

• An obtuse angle is an angle greater than \(90^{\circ}\) but less than \(180^{\circ}\).
• A right angle is an angle equal to \(90^{\circ}\).
• In option B, \(\angle AMB = 90^{\circ}\) and \(\angle BMC=90^{\circ}\). Since \(90^{\circ}+90^{\circ} = 180^{\circ}\) (supplementary angles) and neither angle is obtuse (they are right angles).

Answer:

B.