Question

1. $m\angle 2 = x + 130$

Explanation:

Step1: Use the property of congruent triangles

The two triangles are congruent (marked with equal sides). So, the angle corresponding to \(75^{\circ}\) in the other triangle is equal. And \(\angle2\) is an exterior angle of the triangle.

Step2: Apply the exterior - angle formula

The exterior - angle formula for a triangle states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, \(m\angle2=x + 130\), and using the congruent triangle property and exterior - angle property: \(x+130=75 + 75\)

Step3: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(x = 20\)