Question

m∠m =
m∠n =

Explanation:

Step1: Identify the triangle type

Since \( LM = LN \), \(\triangle LMN\) is an isosceles triangle. In an isosceles triangle, the base angles are equal. But here, \(\angle L = 28^{\circ}\), and we use the angle - sum property of a triangle (\(\angle L+\angle M+\angle N = 180^{\circ}\)).

Step2: Calculate \(\angle M\) and \(\angle N\)

Let \(m\angle M=m\angle N = x\) (because \(LM = LN\), the angles opposite to equal sides are equal).
We know that \(\angle L+\angle M+\angle N=180^{\circ}\). Substitute \(\angle L = 28^{\circ}\) and \(\angle M=\angle N=x\) into the equation:

$$28^{\circ}+x + x=180^{\circ}$$

$$28^{\circ}+2x=180^{\circ}$$

Subtract \(28^{\circ}\) from both sides:

$$2x=180^{\circ}- 28^{\circ}=152^{\circ}$$

Divide both sides by 2:

$$x=\frac{152^{\circ}}{2}=76^{\circ}$$

Answer:

\(m\angle M = 76^{\circ}\), \(m\angle N = 76^{\circ}\)