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### Course: Geometry 227-228 > Unit 1

Lesson 2: Triangle angles- Angles in a triangle sum to 180° proof
- Find angles in triangles
- Isosceles & equilateral triangles problems
- Find angles in isosceles triangles
- Triangle exterior angle example
- Worked example: Triangle angles (intersecting lines)
- Worked example: Triangle angles (diagram)
- Finding angle measures using triangles
- Triangle angle challenge problem
- Triangle angle challenge problem 2
- Triangle angles review

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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 ${180}^{\circ}$ .

*every*triangle add up to**Example:**

*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 ${180}^{\circ}$ , 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:

The missing angle is ${180}^{\circ}$ minus the measures of the other two angles:

${x}^{\circ}={180}^{\circ}-{106}^{\circ}-{42}^{\circ}$ $x=32$

The missing angle is ${32}^{\circ}$ .

*Want to learn more about finding the measure of a missing angle? Check out this video.*

## Want to join the conversation?

- my teacher ask me to do this :/

(up vote if your teacher told you the same thing)(107 votes)- All triangles, no matter the type, are equal to 180 degrees. Unless you take into the degenerative triangle(a hypothetical triangle) which is a triangle whose vertices are on a straight line. In simpler words, it is completely flat. Hope you found this useful(10 votes)

- 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!(46 votes)- 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!(16 votes)

- 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)(9 votes)
- 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(31 votes)

- Are all triangles either right angle, isoceles, or equilateral? what is the trick to figuring out angles to triangles that have all different angles?(7 votes)
- 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.(17 votes)

- Do all Triangle angles always add up to 180 degrees? or is it just the example where the triangles add up to 180 degrees(3 votes)
- Remember that the angle sum of each triangle is always 180 degrees, no matter the triangle type.(17 votes)

- Math is only difficult when you don't understand it. Just keep trying and you'll get it eventually!(9 votes)

- 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.(6 votes)
- 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.(11 votes)

- How do I find a missing value but there's equations in the triangle?(3 votes)
- 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.(15 votes)

- 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.(9 votes)
- Do 37+56 which equals 93 then do 180-93(8 votes)
- you could also do 180 - 37 = 143 and then 143 - 56 which equals 87. This is a different way but it is also longer. JackieE has the quicker way...(3 votes)