How to Find Angle Measures in Triangles

Written by danny waldo
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How to Find Angle Measures in Triangles
These tools can help you calculate the angles of a triangle. (Stockbyte/Stockbyte/Getty Images)

Calculating the measures of angles in a triangle is a fundamental skill in geometry. Triangles can be categorised into three groups: equilateral, scalene and isosceles. Equilateral triangles have three equal sides and angles, isosceles have at least two equal sides and angles, and scalene have no equal sides or angles. However, within these groups, all triangles share two common characteristics: They have the same number of angles (three), and the angles add up to 180 degrees. There are several strategies for determining a triangle's angle measurements, but the strategy you choose is dependent upon the information you have available.

Skill level:

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Things you need

  • Protractor
  • Calculator
  • Pencil
  • Paper

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  1. 1

    Calculate the measure of angles in an equilateral triangle by dividing 180 by 3. The result is 60 degrees. You can prove this equation works because the sum of all angles in a triangle has to equal 180 degrees, and 60 x 3 = 180.

  2. 2

    Find the angle measures of an isosceles triangle by adding the two equal angles together, then, subtracting from 180 to find the missing angle measurement. If you are given the third angle measure and are asked to find the value of the two equal angles, subtract the known measurement from 180 and divide the result by 2 to find the value of the two equal angles.

  3. 3

    Add the measures of two angles and subtract the result from 180 to determine the missing angle of a scalene triangle. Since scalene triangles have no equal sides and no equal angles, you need to know the measure of two of the angles to figure out the measure of the third.

  4. 4

    Use a variable to solve unknown angle measurements when they are presented as a ratio. For example, angles A, B and C may be given as a ratio of 3:5:7. To determine the size of the angles in degrees, multiply each number in the ratio by a common value, such as the variable X. You can now say the smallest angle measure is 3X, meaning the remaining two values are 5X and 7X. Using the equation for finding the value of angle measures (A + B + C = 180), substitute 3X, 5X and 7X for the three angles and you get 15X = 180. Solve for X, and you find its value is 12. Find the angle degrees by substituting 12 for X and multiplying: 3 x 12 = 36, 5 x 12 = 60 and 7 x 12 = 84. The degree measure for the smallest angle is 36, the largest angle is 84 and the remaining angle is 60. Remember, the sum of all of your angles has to equal 180.

Tips and warnings

  • If you do not know the measures of any angles in the triangle, use a protractor to measure one or two angles (depending on the type of triangle). If you have an isosceles triangle, measure the odd angle, then subtract the result from 180 and divide that number by 2 to determine the measures of the other two angles. For a scalene triangle, measure any two angles, then subtract their total from 180 to find the measure of the third angle.

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