Question

question
find ( m angle v x w ).
score 12/15 penalty none
no additional detalls were asked for this assignment.

Explanation:

Step1: Identify the triangle type

Since two sides are equal (marked with the same tick marks), \(\triangle VXW\) is an isosceles triangle. In an isosceles triangle, the base - angles (the angles opposite the equal sides) are equal. Let \(\angle VXW=\angle VWX = x\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). We know that \(\angle V = 45^{\circ}\). So, using the formula \(\angle V+\angle VXW+\angle VWX = 180^{\circ}\). Substituting \(\angle VXW=\angle VWX = x\) and \(\angle V = 45^{\circ}\), we get \(45^{\circ}+x + x=180^{\circ}\).

Step3: Solve the equation for \(x\)

Simplify the equation \(45^{\circ}+2x = 180^{\circ}\). First, subtract \(45^{\circ}\) from both sides: \(2x=180^{\circ}- 45^{\circ}=135^{\circ}\). Then divide both sides by 2: \(x=\frac{135^{\circ}}{2}=67.5^{\circ}\).

Answer:

\(m\angle VXW = 67.5^{\circ}\)