Question

triangles and congruence
if triangle rst is an acute triangle, then m∠s must be

greater than 90° and less than 180°.

equal to 100°.

equal to 90°.

less than 90°.

Explanation:

Step1: Recall acute triangle definition

An acute triangle has all angles less than \(90^\circ\), and the sum of angles in a triangle is \(180^\circ\) (so each angle is also greater than \(0^\circ\), but here we focus on the range for an acute angle).

Step2: Analyze each option

• "greater than \(90^\circ\) and less than \(180^\circ\)": This is an obtuse angle, not acute. Eliminate.
• "equal to \(100^\circ\)": \(100^\circ>90^\circ\), obtuse. Eliminate.
• "equal to \(90^\circ\)": This is a right angle, not acute. Eliminate.
• "less than \(90^\circ\)": Matches the definition of an acute angle (since all angles in acute triangle are acute, i.e., \(<90^\circ\)).

Answer:

less than \(90^\circ\)