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Interior Angle | Corresponding Exterior Angles | Sum of Measures |
---|---|---|
∠11 | ∠1 and ∠2 | m∠1+m∠11=180∘ m∠2+m∠11=180∘ |
∠12 | ∠3 and ∠4 | m∠3+m∠12=180∘ m∠4+m∠12=180∘ |
∠13 | ∠5 and ∠6 | m∠5+m∠13=180∘ m∠6+m∠13=180∘ |
∠14 | ∠7 and ∠8 | m∠7+m∠14=180∘ m∠8+m∠14=180∘ |
∠15 | ∠9 and ∠10 | m∠9+m∠15=180∘ m∠10+m∠15=180∘ |
In contrast, when polygon is concave, some exterior angles might lie inside the polygon. In this case, the measures of those angles are considered to be negative.
In any case, the Polygon Exterior Angles Theorem guarantees that the sum of the measures of the exterior angles is always equal to 360∘.