How to Solve for X in a Trianlge

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Triangle equations are a common part of school geometry and algebra programs. Solving for X in a triangle can encompass a number of different problems. Most commonly, X is used to represent the degree of any one of the three angles found in the triangle. Based on what type of triangle you are trying to solve for and what X represents, there are many different ways to solve for X in a triangle. Graphing the triangle can also help when solving for X.

Determine the Type of Triangle

    Examine the triangle and try to locate a small square marking one of the angles. If there is a square, this is a right triangle and the angle so marked is 90 degrees.

    Look to see if there are two half-circles on the base angles. If it is an isosceles triangle, the two base angles will each have a half-circle with a line through it to denote that these angles are the same size.

    Look to see if there are three half-circles with lines through them at each of the angles. If there are, it is an equilateral triangle, and all three angles are the same size.

Solving for X in a Right Triangle

    Add 90 degrees for the right angle to the degree measurement of the other marked angle. This measurement will be found inside the triangle at the angle that is not denoted by the X variable.

    Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees.

    Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

Solving for X in an Isosceles Triangle

    Locate the two base angles that are marked with half-circles with lines through them. These two angles are the same size.

    Multiply the measurement given for one of the angles by two, if these angles have a measurement given. In this case you are solving for X at the vertex. Subtract the doubled measurement of the angles from 180. This is the value of the X angle at the vertex.

    Subtract the measurement of the vertex angle from 180, if you are only given the measurement of the vertex angle. Divide the difference of the subtraction by two. This will give you the value of X at either of the base angles.

Solving for X in Other Triangles

    Add the given degrees of the two angles provided and subtract that from 180 to solve for X in obtuse and acute triangles.

    Compare the result with the visual representation of the triangle. With obtuse triangles, one angle will be larger than 90 degrees. If you are solving for this angle, be sure the figure you obtain for X is larger than 90 degrees. Acute triangles all have angles smaller than 90 degrees. Be sure that X is smaller than 90 degrees when solving for an acute triangle.

    Determine if the triangle is equilateral by observing the half-circles drawn around all three of the angles with single lines drawn through all of them. If you are dealing with an equilateral triangle, all the angles equal 60 degrees and no additional mathematics is needed to determine the measurements.

    Things You'll Need

    • Calculator
    • Graph paper


About the Author

Tatyana Ivanov has been a freelance writer since 2008 and has contributed articles to "Venus" and "Columbus Family." She continues to write humor pieces for a number of popular culture blogs. Ivanov holds a Bachelor of Arts in media studies from Hunter College.

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