Question

if ( \triangle lmn ) is isosceles, what is the measure of ( angle m )?

Explanation:

Step1: Use the property of isosceles triangle

In an isosceles triangle \( \triangle LMN\), the sides \(LN = MN\) (marked by the tick - marks). So, \(\angle L=\angle M\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(\angle L = \angle M=x\). We know that \(\angle N=126^{\circ}\). Then \(x + x+126^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(2x=180^{\circ}- 126^{\circ}\). So, \(2x = 54^{\circ}\). Divide both sides by 2: \(x=\frac{54^{\circ}}{2}=27^{\circ}\).

Answer:

\(27^{\circ}\)