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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
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!
• 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.
• 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.
• How do I find a missing value but there's equations in the triangle?
• 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 degreesStep 2 | (Total)180 degrees - (A+B)143 degrees = (C)37 degreesAnswer| Angle C equals 37 degrees.