Question

what are the values of v and w?
v =
w =

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle are equal (marked with red lines), the triangle is isosceles. In an isosceles triangle, the angles opposite the equal sides are equal. So \(v = 52^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(v = 52^{\circ}\), then \(v+w + 52^{\circ}=180^{\circ}\). Substitute \(v = 52^{\circ}\) into the equation: \(52^{\circ}+w + 52^{\circ}=180^{\circ}\). Simplify the left - hand side: \(w+104^{\circ}=180^{\circ}\). Solve for \(w\): \(w=180^{\circ}- 104^{\circ}=76^{\circ}\).

Answer:

\(v = 52^{\circ}\), \(w = 76^{\circ}\)