Answer: Triangle LMN is an obtuse triangle.
The angle at vertex L is acute.
The angle at vertex N is acute.
Step-by-step explanation:
Here, triangle LMN has an obtuse angle at vertex M,
Thus, by the definition of obtuse angle triangle LMN is an obtuse triangle,
Now, Angle M is obtuse,
⇒ 90° < m∠ M < 180°
Since, by the property of a triangle,
m∠ L + m∠ M + m∠ N = 180°
⇒ m∠ M = 180° - ( m∠ L+ m∠ N )
⇒ 90° < 180° - ( m∠ L+ m∠ N ) < 180°
⇒ 90° - 180° < - ( m∠ L+ m∠ N ) < 0
⇒ -90° < - ( m∠ L+ m∠ N ) < 0
⇒ 90° > ( m∠ L+ m∠ N ) > 0 ( Since, a < b ⇒ - a > - b)
⇒ 90° > m∠ L and 90° > m∠ N
⇒ Both angle L and angle N are acute.
