Question

what is m∠vwx? m∠vwx = □°

Explanation:

Step1: Use Hypotenuse - Leg Congruence

Since \(YW = YW\) (common side), \(YW = 1\), \(YV = 1\), and \(\angle YVW=\angle YXW = 90^{\circ}\), the two right - angled triangles \(\triangle YVW\) and \(\triangle YXW\) are congruent by the Hypotenuse - Leg (HL) congruence criterion.

Step2: Find the measure of \(\angle VWY\)

In right - angled triangle \(\triangle YXW\), \(\angle XWY = 55^{\circ}\). Because \(\triangle YVW\cong\triangle YXW\), \(\angle VWY=\angle XWY = 55^{\circ}\).

Step3: Calculate \(m\angle VWX\)

Since \(\angle VWX=\angle VWY+\angle XWY\) and \(\angle VWY = \angle XWY=55^{\circ}\), then \(m\angle VWX=55^{\circ}+ 55^{\circ}\)

Answer:

\(110\)