Question

if triangle lmn has an obtuse angle at vertex m, which statements could be true? check all that apply. triangle lmn is an obtuse triangle. the angle at vertex l is acute. the angle at vertex l is right. the angle at vertex n is right. the angle at vertex n is acute. triangle lmn is a right triangle.

Explanation:

Step1: Define obtuse angle property

An obtuse angle > 90°. Sum of triangle angles = 180°.

Step2: Analyze each statement

• Obtuse triangle: Has ≥1 obtuse angle → True.
• ∠L acute: 180° - obtuse ∠M leaves <90° for ∠L+∠N → ∠L can be acute → True.
• ∠L right: 90° + obtuse ∠M >180° → False.
• ∠N right: Same as above → False.
• ∠N acute: ∠L+∠N <90° → ∠N can be acute → True.
• Right triangle: Needs 90° angle, but 90°+obtuse >180° → False.

Answer:

Triangle LMN is an obtuse triangle, The angle at vertex L is acute, The angle at vertex N is acute