Question

what are the values of b and c?

b =

c =

Explanation:

Step1: Use the property of isosceles triangle

Since two sides of the triangle \(VW = VX\) (marked with the same tick), \(\triangle VWX\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let \(\angle V=\ b\), \(\angle X = c\), and \(\angle W=40^{\circ}\). Also, by the angle - sum property of a triangle, \(\angle V+\angle X+\angle W = 180^{\circ}\).

Step2: Set up the equation

Substitute the values into the angle - sum formula: \(b + c+40^{\circ}=180^{\circ}\). Because \(b = c\) (base - angles of an isosceles triangle), we can rewrite the equation as \(2b+40^{\circ}=180^{\circ}\) (or \(2c + 40^{\circ}=180^{\circ}\)).

Step3: Solve for \(b\) and \(c\)

First, solve \(2b+40^{\circ}=180^{\circ}\). Subtract \(40^{\circ}\) from both sides: \(2b=180^{\circ}- 40^{\circ}=140^{\circ}\). Then divide both sides by 2: \(b=\frac{140^{\circ}}{2}=70^{\circ}\). Since \(b = c\), \(c = 70^{\circ}\).

Answer:

\(b = 70\), \(c = 70\)