EZ Math

Geometry · Angles and triangles

How to Find the Angles of an Isosceles Triangle

Problem

vertex angle 40∘\text{vertex angle } 40^\circ

Answer

70∘ each70^\circ \text{ each}

Every triangle has 180 degrees to share. An isosceles triangle gives two equal base angles, so subtract the vertex angle and split what is left.

Step-by-step solution

  1. Use the fact that the base angles are equal.

    B=CB = C

    Why: In an isosceles triangle the two angles opposite the equal sides match.

  2. Subtract the vertex angle from 180.

    B+C=180∘−40∘=140∘B + C = 180^\circ - 40^\circ = 140^\circ

    Why: The three angles of any triangle add to 180 degrees.

  3. Divide the remainder by 2.

    B=C=140∘2=70∘B = C = \frac{140^\circ}{2} = 70^\circ

    Why: The two equal angles share the remainder equally.

Common mistakes

  • Dividing 180 by 3. The triangle is not equilateral.
  • Reporting 140 degrees for each base angle instead of splitting it.
  • Assuming the given angle is a base angle. Here it is the vertex angle.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. vertex angle 100∘\text{vertex angle } 100^\circ

    Show answer

    40∘ each40^\circ \text{ each}

  2. base angle 65∘\text{base angle } 65^\circ

    Show answer

    50∘50^\circ

  3. equilateral triangle\text{equilateral triangle}

    Show answer

    60∘ each60^\circ \text{ each}

  4. base angle 30∘\text{base angle } 30^\circ

    Show answer

    120∘120^\circ

  5. vertex angle 90∘\text{vertex angle } 90^\circ

    Show answer

    45∘ each45^\circ \text{ each}