Posted on April 25, 2022 (Updated on July 24, 2025)

How do you find an exterior side of an exterior angle?

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Finding the Exterior Side of an Exterior Angle: A Friendly Guide

Okay, so exterior angles. They might sound intimidating, but trust me, they’re not as scary as they seem. We bump into them all the time in geometry, especially when we’re wrestling with polygons, triangles, and those sneaky parallel lines. Getting a handle on spotting and figuring them out? Super important for nailing geometry. Let’s break down how to find the exterior side of an exterior angle without getting our brains tied in a knot.

First things first: what is an exterior angle? Simply put, it’s the angle you get when you stretch out one side of a polygon. Imagine you’ve got a triangle, and you decide to make one of its sides longer. That angle that pops up between the long side and the side next to it? Bam! Exterior angle. Each corner, or vertex, of a shape actually has two of these angles, and here’s a cool fact: they always add up to a straight line, which is 180 degrees.

Now, let’s get to the main event: finding that exterior side. Think of it like this: the exterior side is just the part you extended! Here’s how to spot it, step-by-step:

  • Picture the Shape: First, get a good picture in your head of the polygon we’re dealing with. Could be a triangle, a square, or something with a whole bunch of sides.

  • Find the Corner: Next, find the corner (vertex) where you’re trying to locate the exterior angle. Remember, that’s just where two or more lines meet to make a point.

  • Stretch It Out: At that corner, imagine taking one of the lines and making it longer. Usually, in drawings, this extended part is shown as a dashed line, so you know it’s not the original side.

  • Spot the Neighbor: Now, find the side that’s right next to the one you just stretched out. This is the side that makes the original angle at that corner.

  • There’s the Angle: The exterior angle is the space between the stretched-out line and its neighbor.

  • The Winner: And finally, the exterior side? It’s just that stretched-out line itself! That’s it!

    • Calculating the Angle Itself

    Okay, so we’re pros at finding the side, but knowing how to calculate the angle is pretty handy too. Here are a couple of tricks:

  • The Straight Line Trick: Remember how the exterior angle and the angle right next to it make a straight line? That means they add up to 180 degrees. So, if you know the inside angle, just subtract it from 180, and you’ve got the exterior angle. Exterior Angle = 180° – Interior Angle

  • The Remote Control (Interior Angles Theorem): This one’s a bit cooler, especially for triangles. The exterior angle is equal to the sum of the two angles inside the triangle that are not next to it. Exterior Angle = Remote Interior Angle 1 + Remote Interior Angle 2

    • Real-World Examples

    Let’s make this click with a few examples:

  • Equilateral Triangle: All angles are 60 degrees. So, each exterior angle is 180 – 60 = 120 degrees. The exterior side? Just imagine extending any side of the triangle.

  • Square: Each corner is a perfect 90 degrees. That means each exterior angle is 180 – 90 = 90 degrees. And again, the exterior side is just any side extended.

  • Weird Shapes: If you’ve got a shape with crazy angles, you just need to know the inside angle at the corner you’re working with. If that angle is, say, 75 degrees, then the exterior angle is 180 – 75 = 105 degrees. Easy peasy!

    • Watch Out For These Traps!

    • Inside vs. Outside: Don’t mix up the angles inside the shape with the ones you get when you extend a side.
    • Neighbor Troubles: Make sure you’re looking at the side next to the extended one.
    • Theorem Mix-Ups: Double-check you’re using the right trick, especially with triangles.

    Wrapping It Up

    Finding the exterior side of an exterior angle really boils down to knowing what you’re looking at. Picture the shape, find the corner, stretch a line, and you’re golden. Whether you’re tackling homework or just brushing up on your geometry smarts, you’ve now got the tools to handle those exterior angles like a pro. Go get ’em!

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