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?


A.She is correct. A triangle having at least one acute angle is an acute triangle.

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

C.She is incorrect. The angles measure greater than 90 degrees so the triangle is obtuse.

D.She is incorrect. The third angle in a triangle with two congruent acute angles is a right angle.

Answer 1

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

Answer 2

An acute triangle is a triangle with all three angles acute (less than 90°).It is given  The sum of the measures of the two congruent acute angles is greater than 90 degrees. Let the two congruent angles be 46 each .Sum of congruent angles = 46+46=92>90.

If two angles are 46 each then by angle sum property third angle =180-(46+46)=88.THis is true for all values of congruent angles .All angles  of the triangle are less than 90 degrees so the triangle is an acute angles.

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