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Triangle angles review

Review the basics of triangle angles, and then try some practice problems.

Sum of interior angles in triangles

An interior angle is formed by the sides of a polygon and is inside the figure.
The 3 interior angles in every triangle add up to 180, degrees.
Example:
109, degrees, plus, 23, degrees, plus, 48, degrees, equals, 180, degrees
Want to learn more about the interior angles in triangles proof? Check out this video.

Finding a missing angle

Since the sum of the interior angles in a triangle is always 180, degrees, we can use an equation to find the measure of a missing angle.
Example:
Find the value of x in the triangle shown below.
We can use the following equation to represent the triangle:
x, degrees, plus, 42, degrees, plus, 106, degrees, equals, 180, degrees
The missing angle is 180, degrees minus the measures of the other two angles:
x, degrees, equals, 180, degrees, minus, 106, degrees, minus, 42, degrees
x, equals, 32
The missing angle is 32, degrees.
Want to learn more about finding the measure of a missing angle? Check out this video.

Practice

Problem 1
Find the value of x in the triangle shown below.
x, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
degrees

Want to try more problems like this? Check out this exercise

Want to join the conversation?

  • purple pi purple style avatar for user Brynne Van Allsburg
    I do not understand how to find out the angle of x in a when the triangle is in a star shape. Can someone explain that to me?
    Thanks!
    (3 votes)
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    • duskpin ultimate style avatar for user Stefan Henderson
      I know exactly what you mean. In one of the geometry exercises I encountered a problem that might be what you're asking for. I was asked to find x. I had one angle that was 107. I subtracted 107 from 180 and got the remaining amount of 73.By extending one of the lines I was able to find that another angle was 42.Iwas extending the line since it was a transversal going through two parallel lines. Finally I added 107 and 42 together then subtracted their sum by 180 and ended up with my difference and my angle that I was looking for 31.
      (42 votes)
  • aqualine ultimate style avatar for user justin pinks
    can someone explain the theorem better to me? i'm confused and i already watched like all the videos but i still don't get it.(thanks for your time if you do respond)
    (5 votes)
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    • leaf green style avatar for user madiha mariyam
      its basically when u add all the interior(inside)angles of the triangle,the sum is always 180 no matter how big or small the triangles are.
      in the videos sal shows us some examples of sums we may get in exams.
      here r few theorems that may help u
      1 THE SUM OF THE ANGLES OF A TRIANGLE IS ALWAYS 180
      this was explained in the first few videos on
      triangles
      2 THE EXTERIOR ANGLE IS EQUAL TO THE SUM OF TWO INTERIOR OPPOSITE ANGLE
      exterior angle is, the supplementary to that angle (linear pair of angles)
      this means.....imagine a triangle abc the exterior angle of suppose c will be equal to sum of a and b
      sal did few examples of these kind
      3 THE ANGLE OPPOSITE TO LARGE SIDE IS GREATER
      this means the angle opposite to largest side of the triangle is the largest compared to the other two angles
      4 ANGLE OPPOSITE TO SMALLEST SIDE IS LESSER
      this means if the angle is the smallest angle of that triangle the opposite side (to which it is facing )is a small side.So thats why that angle is small
      the same thing with large side (the 3 rd point )
      this theorem or trick was used by sal when he did few examples.
      hope this was helpfull...let me know if what i explained was not what u had asked
      bye
      (3 votes)
  • female robot ada style avatar for user Sureno Pacheco
    In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °, π radians, two right angles, or a half-turn.
    (6 votes)
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  • male robot johnny style avatar for user Mr.beast
    Just keep watching khan academy videos to help you understand or use IXL
    (6 votes)
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  • marcimus purple style avatar for user Nevaeh Brady
    How do I find a missing value but there's equations in the triangle?
    (2 votes)
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    • sneak peak blue style avatar for user 🅻🅸🅶🅷🆃BENDER
      All three angles in any triangle always add up to 180 degrees. So if you only have two of the angles with you, just add them together, and then subtract the sum from 180.
      EX:
      A Triangle has three angles A, B, and C. Angle A equals 60, Angle B equals 84. 
      What is the measure of angle C
      ?

      Step 1| (A)60 degrees + (B)83 degrees = 143 degrees
      Step 2 | (Total)180 degrees - (A+B)143 degrees = (C)37 degrees
      Answer| Angle C equals 37 degrees.
      (7 votes)
  • duskpin seedling style avatar for user Alicia N.W.
    In the ordering triangles exercise it's so hard to find the angles that are smallest & the sides that are smallest. What's the catch?
    (4 votes)
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  • aqualine ultimate style avatar for user Free_Me_Queen_Bee
    Thinking in terms of dimensions proved to be extremely difficult for me throughout my childhood and beyond and I never got to wrap my head around it because I always forced myself to visualize those dimensions. I believe that most of the work here in order to understand this concept and resolve those problems is to let go of your "imaging" brain in a sense, and simply apply the universal algebraic logic to it, as is explained in this video. I'm pretty sure that ultimately you get an intuitive sense of all this with time and practice. I can witness my "tech" coworkers being able to figure these sorts of dimension problems without even thinking about them...
    (4 votes)
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  • blobby green style avatar for user Glenda Perez
    Anytime I am given a shape I pull out colored pencils. You need to shade in or separate out 1 triangle at a time. Start with the one that has 2 of the given angles, add them up and subtract from 180. That should lead you to the next triangle. Repeat the process. Keep your eyes open for any trickes, like congruent sides and/or angles that will shortcut the process.
    (3 votes)
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  • duskpin seedling style avatar for user allison.sugg
    if you are given an angle in a triangle and two of the side lengths, how do you find the other angles?
    (3 votes)
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  • leafers ultimate style avatar for user carternaldridge
    I don't get the star either. I think you're supposed to use the big triangles that are made up of the little ones. I mean the star kind off looks like two triangles overlapped with there bottoms pointed in a little.
    (2 votes)
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    • blobby green style avatar for user Patricia Connors
      Anytime I am given a shape I pull out colored pencils. You need to shade in or separate out 1 triangle at a time. Start with the one that has 2 of the given angles, add them up and subtract from 180. That should lead you to the next triangle. Repeat the process. Keep your eyes open for any trickes, like congruent sides and/or angles that will shortcut the process.
      (2 votes)