111210
AssignmentMultiple Choice

Triangles and Their Side Lengths

Question 111210 • AZ-Geometry A (MA201)

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?

Answer
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.

Explanation

Let each congruent acute angle measure x. Since their sum is greater than 90°, 2x > 90°, so the two angles together measure more than 90°. The third angle is 180° − 2x, which is therefore less than 90°; it is also positive because the angles of a triangle sum to 180°. Thus all three angles are acute, and choice B correctly describes Anna’s conclusion.

AI-written and checked against the verified answer.

Previous
Next