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How Do You Find Missing Angles in an Isosceles Triangle Using Right Triangles?

Find the value of x in the figure

Summary

  1. A 3-sided polygon is a triangle
  2. The little 'o' superscript means 'degrees'
  3. The bar over RS and RT means they are line segments
  4. The equal sign with a squiggly line over it means 'congruent to'
  5. Draw a line down the middle to make two congruent right triangles
  6. The box in the corner of a right triangle represents the 90o angle
  7. The top angle of 32o now becomes two 16o angles
  8. The two bottom angles are equal since we have an isosceles triangle

Notes

    1. Two out of three sides are the same length, so we have an isosceles triangle
    2. 'Congruent' simply means 'the same length'
    1. Creating right triangles will give us known angles of 90o to work with
    2. Isosceles triangles are symmetrical
    3. Drawing a line down the middle will give us two congruent triangles
    1. Setting up an equation will help us solve for 'x', the missing angle
    2. Remember that we split our symmetric triangle in half to get two right triangles
    3. Since we have a right triangle, we know one angle will be 90 degrees
    4. That leaves 90 degrees to be split between the other two angles
    5. Since we know that one of the angles is 16o and the other is 'x', we can write the equation 16+x=90
    1. 'x' is our missing angle
    2. Subtract 16 from both sides to get 'x' by itself
    3. Solving our equation will give us 'x=74o'
    4. We made two congruent triangles when we split the original triangle in half before
    5. So that means the bottom left angle will be equal to the bottom right angle and will also be 74o