Question

1. ( m angle 2 = x + 81 )

Explanation:

Step1: Find the exterior angle of the triangle

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. The angle adjacent to \(127^{\circ}\) is \(180 - 127=53^{\circ}\) (linear pair of angles).

Step2: Use the property of isosceles triangle

The triangle with angle \(\angle2\) is isosceles (two sides are equal). So \(\angle2\) is equal to the angle opposite to the equal side. Using the exterior angle property of the larger triangle (the one with the \(127^{\circ}\) related angle), we know that \(\angle2 = 53^{\circ}\) (because of the isosceles triangle property and angle relationships).

Step3: Solve for \(x\)

Since \(m\angle2=x + 81\) and \(m\angle2 = 53^{\circ}\), we set up the equation \(x+81 = 53\).
Subtract 81 from both sides: \(x=53 - 81=- 28\)

Answer:

\(x=-28\)