Learn on PengiPengi Math (Grade 7)Chapter 7: 2D Geometry and Measurement

Lesson 3: Exterior Angles and Polygons

Property.

Section 1

Defining Exterior Angles of a Triangle

Property

An exterior angle of a triangle is formed when one side of the triangle is extended beyond a vertex. The exterior angle and its adjacent interior angle are supplementary, meaning they sum to 180°180°.

Examples

Section 2

Exterior Angle Theorem

Property

An exterior angle is formed when one side of a triangle is extended outward. It forms a linear pair (summing to 180°) with its adjacent interior angle.

The Exterior Angle Theorem states that the measure of an exterior angle equals the sum of the two non-adjacent (remote) interior angles:

m∠ext=m∠A+m∠Bm\angle\text{ext} = m\angle A + m\angle B

Section 3

Polygon Interior Angle Sum Formula

Property

The sum of interior angles of any polygon with nn sides is given by:

S=(n−2)×180°S = (n-2) \times 180°

This formula is derived by dividing any polygon into (n−2)(n-2) triangles from one vertex.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Defining Exterior Angles of a Triangle

Property

An exterior angle of a triangle is formed when one side of the triangle is extended beyond a vertex. The exterior angle and its adjacent interior angle are supplementary, meaning they sum to 180°180°.

Examples

Section 2

Exterior Angle Theorem

Property

An exterior angle is formed when one side of a triangle is extended outward. It forms a linear pair (summing to 180°) with its adjacent interior angle.

The Exterior Angle Theorem states that the measure of an exterior angle equals the sum of the two non-adjacent (remote) interior angles:

m∠ext=m∠A+m∠Bm\angle\text{ext} = m\angle A + m\angle B

Section 3

Polygon Interior Angle Sum Formula

Property

The sum of interior angles of any polygon with nn sides is given by:

S=(n−2)×180°S = (n-2) \times 180°

This formula is derived by dividing any polygon into (n−2)(n-2) triangles from one vertex.