Question

1. (mangle2 = x + 94)

Explanation:

Step1: Identify triangle property

The triangle has two equal - sides (marked with single - hash marks), so it is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let the angle opposite the marked side with measure \(46^{\circ}\) be equal to the other non - base angle. The sum of the interior angles of a triangle is \(180^{\circ}\).

Step2: Set up an equation

Let \(m\angle2\) be one of the base - angles. We know that \(m\angle2 + m\angle2+46^{\circ}=180^{\circ}\), or \(2m\angle2=180^{\circ}- 46^{\circ}\). So \(2m\angle2 = 134^{\circ}\), and \(m\angle2 = 67^{\circ}\).

Step3: Solve for \(x\)

Since \(m\angle2=x + 94\), then \(x+94 = 67\). Subtract 94 from both sides: \(x=67 - 94=-27\).

Answer:

\(x=-27\)