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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

## 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.

## Practice

Problem 1
• Current
Find the value of x in the triangle shown below.
x, equals
degrees

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

## Want to join the conversation?

• 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!
• 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!
• my teacher ask me to do this :/

(up vote if your teacher told you the same thing)
• 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)
• 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.
bye
• 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.
• 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...
• 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.
• 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.
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 degreesStep 2 | (Total)180 degrees - (A+B)143 degrees = (C)37 degreesAnswer| Angle C equals 37 degrees.