In this video, we are going to look at the angle relationships in a triangle.

Let’s label the angles , , and . The most common rule for angles in a triangle is:

If we extend one side (past angle c as shown in the video) and label it , then there is another rule, which works for all exterior angles.

**For example:**

If and , then must be . Since , then must be because they lie on a straight line. Therefore, .

## Video-Lesson Transcript

In this lesson, we’ll cover angle relationships in a triangle.

A triangle has three angles.

Let’s label them as , , and .

If we add this all up:

If we extend the horizontal line of the triangle going to the right, we will form a new angle. Let’s call this angle .

Let’s give values to this:

Since , should be because and forms

This is also because:

and

remains the same in both situations so .

This is true for any of these.

If you will extend the horizontal line of the triangle going to the left, let’s label this .

Then

So, if and , therefore .

In this case, we proved that .

Now, let’s extend the line with angle and call it angle .

Since , the angle beside it is .

Therefore,

The sum of all the interior angles is equal to .

And the exterior angles is equal to the sum of the other two interior angles.

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