Question

triangle def contains two congruent acute angles. the sum of the measures of the two congruent acute angles is greater than 90 degrees. anna concludes that the triangle must be an acute triangle. which best describes her conclusion?
○ she is correct. a triangle having at least one acute angle is an acute triangle.
○ she is correct. the remaining angle of the triangle measures less than 90 degrees.
○ she is incorrect. the angles measure greater than 90 degrees so the triangle is obtuse.
○ she is incorrect. the third angle in a triangle with two congruent acute angles is a right angle.

Explanation:

Step1: Sum of triangle angles

The total sum of angles in a triangle is $180^\circ$.

Step2: Calculate the third angle

Let the two congruent acute angles sum to $S > 90^\circ$. The third angle is $180^\circ - S < 90^\circ$.

Step3: Determine triangle type

All three angles (two congruent acute angles + third angle < 90°) are acute.

Answer:

She is correct. The remaining angle of the triangle measures less than 90 degrees.