Question

1. ( mangle2 = x + 94 )

Explanation:

Step1: Use the property of congruent triangles

Since the two triangles are congruent (marked with equal - side symbols), the angle corresponding to the \(47^{\circ}\) angle in the lower - left triangle is equal to \(47^{\circ}\) in the upper - right triangle. Then, using the angle - sum property of a triangle (the sum of angles in a triangle is \(180^{\circ}\)), for the right - angled triangle (assuming it's a right - angled triangle formed by the congruent sides and the angle \(m\angle2\)), we know that \(m\angle2=180^{\circ}- 2\times47^{\circ}\).

$$m\angle2 = 180 - 94$$

$$m\angle2=86^{\circ}$$

But if we use the given equation \(m\angle2=x + 94\) and assume there is a mis - understanding in the problem (maybe it's an isosceles triangle property application). If we consider the exterior - angle or some other property (assuming the problem is about solving for \(x\) given \(m\angle2\) value). If \(m\angle2 = 106^{\circ}\) (as written in purple), then:

Step2: Solve for \(x\)

Given \(m\angle2=x + 94\), substitute \(m\angle2 = 106\)

$$106=x + 94$$

Subtract 94 from both sides:

$$x=106 - 94$$

$$x = 12$$

Answer:

\(x = 12\)