Math CC7/8 – Sept. Things Needed Today (TNT): Math Notebook/Pencil/Angle Ruler or Protractor Math Book –Shapes & Designs 2.4 Labsheet 2.4 A&B (located on table by the door) Learning Log: Topic: Ins & Outs of Polygons HW: S &D pg.54 #12, 14, 15 & Triangle WS

What’s Happening? Warm Up Lesson- S&D 2.4! Start Homework

Warm-Up WRITE down each problem & SOLVE Show ALL your work & THINKING How many individual angles in a decagon? Calculate the total sum of the interior angles of a decagon. Evaluate the formula for n = 10. (n - 2)180° (10 - 2)180° 8 x 180° 1,440° A decagon has 1440°.

2.4 The Ins & Outs of Polygons Take Notes Familiar figures like triangles, parallelograms & trapezoids are called convex polygons. A convex polygon is a polygon with all its individual interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Figures like the star and the arrowhead pictured below are called concave polygons. A concave polygon is a polygon with one or more interior angles greater than 180°. It looks sort of like a vertex has been 'pushed in' towards the inside of the polygon. Shapes & Designs, p. 49

By extending the sides of a convex polygon, 2.4 cont…. For convex polygons it is clear which points are on the inside and which are on the outside. It is also clear how to measure interior angles (inside of the polygons). By extending the sides of a convex polygon, you can make an exterior angle that lies outside the polygon.

2.4 cont…. The figures below show 2 ways to form exterior angles. You can extend the sides as you move in either direction around the polygon. Measuring exterior angles can provide useful information about the interior angles of polygon.

If finish, begin 2.4 B

The Exterior Angles of a Polygon add up to 360°

Exterior Angles of Polygons Interior Angles Exterior Angles Use your protractor to measure the exterior angles of these shapes. Make a statement about your findings. ? 180o Exterior angles of a polygon sum to 360o.

Sum of the INTERIOR angles is: S = (n -2) 180 S = (5 – 2) 180 or S = 3(180) Sum of the EXTERIOR angles is 360 , but we can view that as 2(180) So… total sum of interior and exterior angles (T) is: T = 3(180) + 2(180) or T = (3+2)180 T = 180(5)

T = 180n – 360 is the total interior angle measure. The 360 can be thought of as 180(2). T = 180n – 180(2) Using the Distributive Property, we can now see that we have the formula developed in lesson 2.2, which is T = (n-2)180

3(180) 360 3(180) – 360 = 180 Total – exterior = interior

x + 2x + 3x = 180 6x = 180 6 6 x = 30 x = 30, 2x = 60, 3x = 90 Supplements: x + 2x + x – 20 = 180 4x - 20 = 180 4x = 200 4 4 X = 50, 2x = 100, x – 20 = 30 Supplements:

S&D p. 54 #12, 14, 15 & Triangle Worksheet (SHOW ALL WORK) Start Homework S&D p. 54 #12, 14, 15 & Triangle Worksheet (SHOW ALL WORK)