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Interior & Exterior Angles Calculator

QUICK LINKS


Interior & Exterior Angles Calculator

Interior and Exterior Angles of Polygons

CALCULATOR

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 .
We have some questions for you! Help us out through this
INTRO
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 explore our
Lesson
and
Practice
sections to learn more about how to find the area of triangles and test your understanding.

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KEY STEPS

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:
LESSON
Interior Angles
PRACTICE
Interior Angles
LESSON
Exterior Angles
PRACTICE
Exterior Angles
CONCLUSION
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