# Who Proved Polygon Exterior Angle Sum Theorem?

## Polygon Exterior Angle Sum Theorem

### Who invented exterior angle theorem?

Euclid's exterior angle theorem The proof of Proposition 1.16 given by Euclid is often cited as one place where Euclid gives a flawed proof.

### What is the proof for the exterior angle theorem?

Proof of Exterior Angle Theorem

StatementReason
∠a = ∠x Pair of alternate angles. (Since BA is parallel to CE and AC is the transversal).
∠b = ∠y Pair of corresponding angles. (Since BA is parallel to CE and BD is the transversal).
∠a + ∠b = ∠x + ∠y From the above statements
∠ACD = ∠x + ∠y From the construction of CE

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### How do you prove polygon angles sum theorem?

Theorem: The sum of the angles in any convex polygon with n vertices is (n – 2) · 180°. Proof: By induction. Let P(n) be “all convex polygons with n vertices have angles that sum to (n – 2) · 180°.” We will prove P(n) holds for all n ∈ ℕ where n ≥ 3.

### What is the exterior angle sum property of polygon?

360 degreesThe sum of exterior angles in a polygon is always equal to 360 degrees. Therefore, for all equiangular polygons, the measure of one exterior angle is equal to 360 divided by the number of sides in the polygon.