Exterior Angle Theorem Background
So. most of us know that a straight-line measures 180 degrees. When two angles form to create a straight line, they, too, measure 180 degrees. Suppose I informed you that there is a cool mathematical trick that you can utilize when working with a triangular that uses this easy reality? So, let’s learn more about the exterior angle theorem.
Currently, before you obtain all anxiety over the concept that this lesson has to do with a thesis, know that in this situation, an idea is just the fancy means of saying policy. You can go on and breathe a sigh of alleviation to know that we aren’t most likely to function through any two-column evidence or attempt to show this theorem by the opposition. Instead, we will concentrate on the formula itself and also precisely how we can apply the theorem to fix for missing angles of a triangle.
Definition & Solution
The Exterior angle theorem states that the Exterior angle developed when you prolong a triangular side is equal to its non-adjacent angles. Remember, our non-adjacent angles are those that do not touch the angle we are dealing with. So, when we prolong a curve’s side, producing a straight line that exceeds the triangular. We have created an Exterior, or Exterior, angle that equates to both angles within the triangular that it does not touch.
Let’s consider complying with representation to place this in simpler terms.
Diagram of a triangle with an Exterior angle
The exterior angle theorem tells us that angle D’s step is equal to the sum of angles and B.
In formula kind: m< D = m< A + m< B.
Reflect on our specific the fact that a straight line amounts to 180 levels. We should also remember that the angles of a triangle equal 180 levels too.
m< A + m< B + m< C = 180.
m< C + m< D = 180.
You could observe that each formula amounts to 180. As a result of this, you can set them equal to.
m< A + m< B + m< C = m< C + m< D.
Currently, cancel out them? Hence, it appears on both sides of our formula to simplify it.
m< A + m< B = m< D.
And quickly, we are back to our initial formula for the exterior angle Theorem. It is that simple. Currently, it’s not likely that you will ever need to show this theorem truly, but it is always good to comprehend why something functions before you begin using it.