Answer:
m∠M=24°
Step-by-step explanation:
The sum of all the angles of the triangle is equal to 180°. It is given that Triangle ABC is similar to triangle LMN by the AA similarity postulate, therefore, similar triangles have similar set of angles. If ∠A=108°, then ∠L will also be equal to 108°, ∠B=∠M and ∠C=∠N by similarity of the triangles.
Now, let ∠M=x, then ∠B=x, also it is given that ∠C=2∠M, therefore by the sum property of the triangles,
∠A+∠B+∠C=180°
⇒108°+x+2x=180° (because ∠C=2∠M=2x)
⇒3x+108°=180°
⇒3x=180°-108°
⇒3x=72°
⇒x=24°
Therefore, m∠M=24°
