Question

1. $m\angle 2=x + 43$

Explanation:

Step1: Use triangle angle sum property

The left - hand triangle has a \(60^{\circ}\) angle and a \(90^{\circ}\) angle. So the third angle is \(180-(60 + 90)=30^{\circ}\).

Step2: Use congruent triangles property

The two triangles are congruent (by SSS as two sides are equal and the included right angles are equal). So \(m\angle2=30^{\circ}\).

Step3: Solve for \(x\)

Set \(x + 43=30\). Then \(x=30 - 43=-13\).

Answer:

\(x=-13\)