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Interior & Exterior Angles in the House 🏠

QUICK LINKS


Interior & Exterior Angles in the House 🏠

Interior & Exterior Angles in the House! 🏠

The interior angles of a polygon are angles inside the shape. The exterior angles of a polygon are angles outside of the shape formed between any side of the polygon and a line extended from the side next to it.
If we imagine the polygon as a house, the interior angles live inside of the house, while the exterior angles live in exile outside of the house.
We can find the sum of interior angles in a shape with sides using the formula:Just remember that a triangle has , and we can fit triangles in a shape with sides.The sum of exterior angles for all simple polygons is always - see how they form a circle when we combine them?We can use these sums to solve for missing angles inside and outside of polygons. Check out our calculator or continue the lesson to explore interior & exterior angles in more detail!

Interior & Exterior Angles Calculator

Step 1. Determine whether you’re looking for interior or exterior angles.

If we think of the shape as a house, the interior angles live inside of the house, while the exterior angles live in exile outside of the house.
Pick which type of angles you’re looking for.

Step 2. Calculate the sum of angles.

The sum of exterior angles for all polygons is always .This animation ⬆️ can help you see how the exterior angles combine to create a circle, which is .

Step 3. Find the value of an individual angle.

How many sides does the shape have?
Is the shape regular? This means all the sides are the same length.
We can help you out if you know all but one exterior angle. What are the other -1 angles?
Since the sum of the exterior angles is , we just need to subtract the given angle values to find the unknown angle:
The unknown angle is .

Recap 🧢: How to Find the Interior & Exterior Angles of Polygons

Step 1. Determine whether you’re looking for interior or exterior angles.

If we imagine the polygon as a house, the interior angles live inside of the house, while the exterior angles live in exile outside of the house.Type of Angles:

Step 2. Count the number of sides () the shape has.

Step 3. Calculate the sum of interior angles.

Step 4. Find the value of an individual angle.

If your shape is regular, just divide the sum of the interior angles by the number of sides/angles:
If your shape is irregular and you have the values of all the other interior angles, you can find the missing angle by subtracting your given angles from the sum:

Step 2. Calculate the sum of exterior angles.

The sum of exterior angles for all shapes is always .

Step 3. Find the value of an individual angle.

If your shape is regular, just divide the sum of the exterior angles by the number of sides/angles:
If your shape is irregular and you have the values of all the other exterior angles, you can find the missing angle by subtracting your given angles from the sum:
Learn more about interior & exterior angles. Pick where you want to start!
You can also use the Quick Links menu to jump to the section you’d like to explore!
When you feel like you've mastered this lesson, click for a celebration ⬇️!
Dang, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?