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