1. Daily Warm-Up Quiz 3 minutes 1.The sum of the measures of the interior angles of any triangle is ___________. 2.If two angles of one triangle are congruent to two angles of another triangle, then their third angles _____. 3.A diagonal is a segment ___________. 4.A regular polygon is ______________. 5.x = -?-. 84 48 x

2. Polygon Sum Conjecture During this lesson, we will:  Find the sum of measures of the interior angles of a quadrilateral  Determine and apply a formula for finding the sum of the measures of the interior angles of any polygon  Determine and apply a formula for finding the measure of one angle in a regular (equilateral/equiangular) polygon

3. INVESTIGATION Group I Group II Find the sum of the measures of the four angles of your pre-cut quadrilateral, using your protractor. Compare your answer with Group II members. Group II Group I Find the sum of the measures of the four angles of your pre-cut quadrilateral by tearing off the four angles,  Q,  U,  A, and  D and arranging them about a point. Compare your answer with Group I members.

4. Quadrilateral Sum Conjecture What appears to be true each time? State your next conjecture. Illustrate this in your glossary. The sum of the measures of the interior angles of any quadrilateral is _____. 360 

5. INVESTIGATION Use the table provided in your guided notes to find a formula that relates the number of sides of a polygon and the total number of in its angles. What about the other polygons?

6. POLYGON INTERIOR ANGLES SUM CONJECTURE POLYGON SUM: POLYGON SUM: ______________ ____________________________ ____________________________ ____________________________. The sum of the interior angles of any n-gon is (n-2) 180 (n-2) 180, where n is the number of sides.

7. Recall: An equiangular polygon is a polygon with all angles equal in measure. An equilateral polygon is a polygon with all sides equal in length. A regular polygon is a polygon with all its angles equal in measure and all its side equal in length. In other words, it is a(n) ______________________________. equiangular and equilateral polygon

8. Use the table to help you predict the measure of each angle in an equiangular polygon. # Sides34567…n  s Sum Each  The measure of each angle in an equiangular n-gon is ________. (n-2) 180 n

9. Final Checks for Understanding Given: Regular Hexagon Find: x x 76 104 76 y Find y.