Question

if triangle rst is an acute triangle, then ( mangle s ) must be
less than ( 90^{circ} ).
equal to ( 90^{circ} ).
equal to ( 100^{circ} ).
greater than ( 90^{circ} ) and less than ( 180^{circ} ).

Explanation:

Step1: Recall the definition of an acute triangle

An acute triangle is a triangle in which all angles are less than \(90^{\circ}\).

Step2: Analyze each option

• Option 1: If \(m\angle S\) is less than \(90^{\circ}\), it is consistent with the definition of an acute triangle.
• Option 2: If \(m\angle S = 90^{\circ}\), the triangle is a right - triangle, not an acute triangle.
• Option 3: If \(m\angle S=100^{\circ}\), since \(100^{\circ}>90^{\circ}\), the triangle is an obtuse triangle.
• Option 4: Angles greater than \(90^{\circ}\) and less than \(180^{\circ}\) are obtuse angles. A triangle with an obtuse angle is an obtuse triangle.

Answer:

less than \(90^{\circ}\)