How to Find Angles in an Isosceles Triangle

Find the measure of angles by learning the properties of base and vertex angles.

Isosceles triangles consist of two congruent (same size) sides called legs and one side that has a different measure, called the base. The angles formed at where the legs meet the base of the triangle on the left and right sides are congruent and referred to as the base angles. The vertex angle, defined by where the two legs meet each other offers a different measure than the base angles. The angles of a triangle must add up to 180 degrees. Finding the measurement of one angle helps you calculate the degrees of the other two angles through the use of algebra, number sense and geometry skills.

Instructions

1. Look at the isosceles triangle given in the problem you are trying to solve or draw an isosceles triangle, if you're reading a word problem that does not provide a pictoral representation of the triangle. Underline words in the problem like vertex angle or base angle.

2. Label the vertex angle "a" and the base angles, "b" and "c," if not already labeled. Note that angles "b" and "c" will be the same amount of degrees.

3. Reread the word problem or look at the picture to extract information about angle measurements. If two different angle measurements are given, add them together. Subtract the total from 180 degrees to find your third angle measurement. For example, add 90 degrees and 45 degrees together, as indicated in such a problem, to get 135 degrees. Subtract 135 degrees from 180 degrees to find the missing angle of 45 degrees. This shows you that the two congruent base angles are each worth 45 degrees and the vertex angle is worth 90 degrees.

4. Subtract the measure of the vertex angle, if only given this measurement, from 180 degrees. Divide the answer by 2 to find the congruent measurements of the base angles. For example, subtract a vertex angle of 100 degrees from 180 degrees to find 80 degrees leftover. Divide 80 degrees by 2 to find that each base angle is worth 40 degrees.

5. Manipulate an isosceles triangle problem, if only given the measurement of one base angle by doubling the amount and subtracting it from 180 degrees to find the measurement of the vertex angle. For example, if given a base angle measurement of 40, add 40 to account for the other congruent base angle to get 80 degrees in total base angle measurements. Subtract 80 from 180 to calculate the vertex angle as 100 degrees.

References

• Think Quest: Isosceles and Equilateral Triangles
• Regents Prep: Isosceles Triangle Theorums
• Wolfram Math World: Isosceles Triangle
• Math Teacher: Angle Sum of a Triangle