CALCULATOR

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## 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

__in__terior angles live__in__side of the house, while the__ex__terior angles live in__ex__ile outside of the house.Pick which type of angles you’re looking for.

We have some questions for you! Help us out through this

INTRO

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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

__in__terior angles live__in__side of the house, while the__ex__terior angles live in__ex__ile outside of the house.KEY STEPS

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## How to Find the Interior & Exterior Angles of Polygons

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

If we think of the shape as a house, the

Type of Angles: __in__terior angles live__in__side of the house, while the__ex__terior angles live in__ex__ile outside of the house.### Step 2. Count the number of sides ($n$) the shape has.

### Step 3. Calculate the sum of interior angles.

For any convex shape with $n$ sides, $n−2$ triangles fit inside. For example, $5−2=3$ triangles fit inside a shape with $5$ sides.

And since the angles in a triangle always add up to $180_{∘}$, the sum of the interior angles is equal to $a triangledegrees in 180_{∘} ×# of triangles(n−2) $.

$sum of interior angles =180_{∘}×(n−2)=180_{∘}×(n−2) $

### 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:

$each interior angle =nsum of interior angles =n180_{∘}×(n−2) $

**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:

$unknown angle =sum of interior angles−sum of given interior angles=180_{∘}×(n−2)−sum of given interior angles $

LESSON

— Interior Angles

PRACTICE

— Interior Angles

LESSON

— Exterior Angles

PRACTICE

— Exterior Angles

CONCLUSION

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