-free- Unit 8- Polygons And Quadrilaterals Homework 1- Angles Of Today

The sum of interior angles is ( 2340^\circ ). Find ( n ).

Each interior angle of a regular polygon is ( 140^\circ ). How many sides does it have? The sum of interior angles is ( 2340^\circ )

Welcome to the first homework assignment of Unit 8! In this lesson, we focus on the interior and exterior angles of polygons . Mastering these formulas will build the foundation for understanding more complex quadrilaterals and polygon properties later in the unit. Key Concepts to Remember 1. Interior Angle Sum Formula For any polygon with ( n ) sides: [ \text{Sum of interior angles} = (n - 2) \times 180^\circ ] 2. Each Interior Angle (Regular Polygon) For a regular polygon (all sides and angles equal): [ \text{Each interior angle} = \frac{(n - 2) \times 180^\circ}{n} ] 3. Exterior Angle Sum The sum of exterior angles of any polygon (one per vertex, extended in the same direction) is: [ \text{Sum of exterior angles} = 360^\circ ] 4. Each Exterior Angle (Regular Polygon) [ \text{Each exterior angle} = \frac{360^\circ}{n} ] Worked Examples Example 1: Find the sum of interior angles of a decagon (10 sides). How many sides does it have

[ (n - 2) \times 180 = (10 - 2) \times 180 = 8 \times 180 = 1440^\circ ] Mastering these formulas will build the foundation for

First, find each exterior angle: ( 180 - 140 = 40^\circ ) Then, ( n = \frac{360}{40} = 9 ) sides.