if triangle rst is an acute triangle, then ( mangle s ) must be\nless than ( 90^{circ} ).\nequal to (…

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

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

Answer

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})