# Angle Relationships In Triangles

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

Let’s label the angles $a\textdegree$, $b\textdegree$, and $c\textdegree$. The most common rule for angles in a triangle is:
$a\textdegree + b\textdegree + c\textdegree = 180\textdegree$

If we extend one side (past angle c as shown in the video) and label it $d\textdegree$, then there is another rule, which works for all exterior angles.$a\textdegree+b\textdegree=d\textdegree$

For example:
If $a\textdegree=60\textdegree$ and $b\textdegree=70\textdegree$, then $c\textdegree$ must be $50\textdegree$. Since $c=50\textdegree$, then $d$ must be $130\textdegree$ because they lie on a straight line. Therefore, $a\textdegree+b\textdegree=d\textdegree$.

## Video-Lesson Transcript

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

A triangle has three angles.

Let’s label them as $a^{\circ}$, $b^{\circ}$, and $c^{\circ}$.

If we add this all up:

$a^{\circ} + b^{\circ} + c^{\circ} = 180$

If we extend the horizontal line of the triangle going to the right, we will form a new angle. Let’s call this angle $d^{\circ}$.

$a^{\circ} + b^{\circ} = d^{\circ}$

Let’s give values to this:

$a^{\circ} = 60^{\circ}$
$b^{\circ} = 70^{\circ}$
$c^{\circ} = 50^{\circ}$

Since $c^{\circ} = 50^{\circ}$, $d^{\circ}$ should be $130^{\circ}$ because $c$ and $d$ forms $180^{\circ}$

This is also because:

$a + b + c = 180$
and
$c + d = 180$

$c$ remains the same in both situations so $a + b = d$.

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 $f^{\circ}$.

Then $b + c = f$

So, if $a = 60^{\circ}$ and $a + f = 180$, therefore $f = 120^{\circ}$.

In this case, we proved that $b + c = f$.

Now, let’s extend the line with angle $b$ and call it angle $g^{\circ}$.

Since $b = 70^{\circ}$, the angle beside it is $110^{\circ}$.

Therefore, $a + c = g$

The sum of all the interior angles is equal to $180$.

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