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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.
Example:
A triangle. The bottom, left angle measure is 48 degrees. The top, left angle measure is 109 degrees. The top, right most angle measure is 23 degrees.
109+23+48=180
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, we can use an equation to find the measure of a missing angle.
Example:
Find the value of x in the triangle shown below.
A triangle. The top, left angle measure is x degrees. The top, right most angle measure is 42 degrees. The bottom, right most angle measure is 106 degrees.
We can use the following equation to represent the triangle:
x+42+106=180
The missing angle is 180 minus the measures of the other two angles:
x=18010642
x=32
The missing angle is 32.
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=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
A triangle. The top, left angle measure is 37 degrees. The top, right most angle measure is 56 degrees. The bottom, right most angle measure is x 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!
    (42 votes)
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    • starky seed style avatar for user 20022825
      well this was two years ago so i'm sure you don't still need help, but in case you do or for other people, when its a star the two angles they give you are a part of a triangle inside the star. So you add those and subtract from 180 to get the third angle, so X would be 180-? to get that third angle. X would be the number you originally subtracted from 180. Hope that helps!
      (14 votes)
  • hopper cool style avatar for user .
    my teacher ask me to do this :/

    (up vote if your teacher told you the same thing)
    (63 votes)
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  • 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)
    (8 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
      (26 votes)
  • blobby green style avatar for user leela.m.desai
    Are all triangles either right angle, isoceles, or equilateral? what is the trick to figuring out angles to triangles that have all different angles?
    (5 votes)
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    • mr pink green style avatar for user David Severin
      You can classify angles by sides or angles, and you are mixing these two up. By sides, you can have equilateral (3 equal sides - this can also be called equiangular because all angles are 60 degrees), isosceles (two equal sides), or scalene (no equal sides - this would be your situation of all different angles). By angles, you have acute (all angles less than 90), right (one 90 degree angle), or obtuse (one angle greater than 90).
      There is also a theoretical triangle called a degenerative triangle which forms a straight line, but that will not come until much higher math.
      (15 votes)
  • leafers ultimate style avatar for user Boulgab
    Do all Triangle angles always add up to 180 degrees? or is it just the example where the triangles add up to 180 degrees
    (2 votes)
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  • starky seedling style avatar for user Gonzalez, Jason; 201111834
    why math hard
    (8 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.
    (5 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.
      (9 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.
    (8 votes)
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  • blobby green style avatar for user JackieE
    Do 37+56 which equals 93 then do 180-93
    (7 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.
      (13 votes)