6-1 A NGLES OF A P OLYGON. POLYGON: A MANY ANGLED SHAPE SidesName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 8Octagon 10Decagon nn-gon # sides = # angles.

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Presentation transcript:

6-1 A NGLES OF A P OLYGON

POLYGON: A MANY ANGLED SHAPE SidesName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 8Octagon 10Decagon nn-gon # sides = # angles = #vertices

S OME I NFO : Regular Polygon: all angles are equal Diagonal: a segment connecting 2 nonconsecutive vertices.

DIAGONALS (Look at these, don’t write in notes) Quadrilateral Look! 2 triangles 2(180) = 360 Sum of the angles of a quadrilateral is 360 Pentagon 3 triangles 3(180) = 540 Sum of the angles of a pentagon is 540 What do you think about a hexagon? 4(180) = 720 SO

T HEOREM The sum of the measures of the INTERIOR angles with n sides is (n – 2)180 The sum of the measures of the exterior angles of any polygon is 360. ALWAYS 360!!

TWAP—(T RY WITH A P ARTNER ) H INT : J UST P LUG INTO THE FORMULA ! Find a) the sum of the interior angles and b) the sum of the exterior angles for each shape 1) 32-gon2) Decagon Answers: 1)a) 5400b) 360 2)a) 1440b) 360

Other Formulas… The measure of EACH EXTERIOR angle of a regular polygon is: 360 n (It’s 360 divided by the number of sides) The measure of EACH INTERIOR angle of a polygon is: (n-2)180 n (It’s the SUM of Interior divided by # of sides)

Example Find the measure of EACH interior angle of a polygon with 5 sides. (5-2) (180)= /5 = 108

E XAMPLE Find the measure of each interior angle of parallelogram RSTU. Since the sum of the measures of the interior angles is Step 1Find the sum of the degrees!

E XAMPLE CONT. Sum of measures of interior angles

E XAMPLE CONT Step 2Use the value of x to find the measure of each angle. Answer: m  R = 55, m  S = 125, m  T = 55, m  U = 125 mR=5xmR=5x =5(11)= 55 m  S=11x + 4 =11(11) + 4 = 125 mT=5xmT=5x =5(11)= 55 m  U=11x + 4 =11(11) + 4 = 125

To Find # of sides… Formula: ____360____ 1 ext. angle (360 divided by 1 ext angle) Also: 1 interior angle + 1 exterior angle = 180

Example How many sides does a regular polygon have if each exterior angle measures 45º? n = 8 sides

E XAMPLE How many sides does a regular polygon have if each interior angle measures 120º? Find ext angle: = n = 6 sides

E XAMPLE Find the value of x in the diagram.

How many degrees will it =? Answer:x = 12 5x + (4x – 6) + (5x – 5) + (4x + 3) + (6x – 12) + (2x + 3) + (5x + 5)=360 (5x + 4x + 5x + 4x + 6x + 2x + 5x) + [(–6) + (–5) (–12) ]=360 31x – 12=360 31x=372 x=12

E QUATIONS TO K NOW (F LASHCARDS !!!!) Sum of interior angles Each interior angle Sum of exterior angles Each exterior angle # of Sides

H OMEWORK Pg. 398 #13-37 odd, 49