How to Find Triangle Angle Measurements

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The sum of the three angles in a triangle always equals 180 degrees. The triangle may be right, isosceles, acute, obtuse, equilateral or scalene, yet the sum of all the angles is still 180 degrees. Use the properties from each type of triangle to solve the question of angle measurement. When you keep these specific characteristics in mind, it's a matter of accurately computing the angle measurement.

Two Known Angles

  • Draw a triangle if the image is not provided. Label each known angle with the corresponding measurements.

  • Add the two measurements together.

    Example:

    Angle A: 30 degrees

    Angle B: 45 degrees

    30 + 45 = 75

  • Subtract the total of the two measurements from 180 degrees to find the measure of the third angle.

    180 - 75 = 105

    Angle C = 105 degrees

  • Add the answer and the two supplied angle measurements to check for accuracy. The sum of all three angles should equal 180 degrees.

    30 + 45 + 105 = 180 degrees

One Known Angle

  • Draw a triangle if the image is not provided. Isosceles and right triangles are common triangles used when one angle measurement is supplied. Label each known angle with the supplied measurement.

  • Form an equation, using the properties of the type of triangle presented in the problem that equals 180 degrees. Isosceles triangles contain equal angle measurements adjacent to the equal length sides while right triangles contain one 90-degree angle.

    Isosceles Example:

    Angle A (adjacent to equal side angle) = x

    Angle B (adjacent to equal side angle) = x

    Angle C = 80 degrees

    x + x + 80 = 180

    Right triangle example:

    Angle A = right angle = 90 degrees

    Angle B = 15 degrees

    Angle C = x

    90 + 15 + x = 180 degrees

  • Solve the equation for the value of "x" by subtracting the digits from 180 degrees.

    Isosceles example:

    x + x + 80 = 180

    2x = 100

    x = 50

    Right triangle example:

    90 + 15 + x = 180 degrees

    105 + x = 180 degrees

    x = 75 degrees

  • Add the computed and supplied angle measurements to ensure it equals 180 degrees.

    Isosceles example:

    50 + 50 + 80 = 180 degrees

    Right triangle example:

    90 + 15 + 75 = 180 degrees

No Known Angles

  • Sketch an equilateral triangle, which is a polygon with three equal sides and three equal angles. Label each angle measurement with an "x" representing the unknown measurement.

  • Form an equation adding the three unknown measurements equaling 180 degrees, which is the sum of all three angles in any type of triangle.

    Angle A = x

    Angle B = x

    Angle C = x

    x + x + x = 180

  • Solve the equation for "x" by combining the three values to "3x." And then divide each side of the "equals" sign by three.

    3x = 180

    x = 60 degrees

  • Check your work by adding each angle measurement together and comparing the sum to 180 degrees.

    60 + 60 + 60 = 180 degrees

References

  • Photo Credit Hemera Technologies/PhotoObjects.net/Getty Images
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