If one base angle of an isosceles triangle measures 70°, what is the measure of the vertex angle?

Explanation

We will use the isosceles triangle theorem and the fact that the sum of the angle measures of any triangle is 180° to write an equation that models the situation. We can then solve the equation to find the unknown angle measure.

By the isosceles triangle theorem, if one of the base angles measures 70°, so does the other. (See the figure on the right.) If we let represent the measure of the vertex angle, we have

• The sum of the measure of the angles of a triangle is 180°
  • \(x + 70^o + 70^o = 180^o\)
• Combine like terms: 70° + 70° = 140°
  • \(x + 140^o = 180^o\)
• To isolate x, undo the addition of 140° by subtracting 140° from both sides.
• \(x = 40^o\)

The vertex angle measures 40°