Determine each of the following: U10D1 Have Out: GP NB, Pencil, highlighter, Red Pen Determine each of the following: Bellwork: 1. The measure of each interior angle in a regular 18-gon. (n – 2)180 n m of 1 int  of a regular n-gon = +1 (18 – 2)180 18 = = 160 +1 2. The measure of each exterior angle of a 16-gon. You can not do this problem! The figure must be regular in order to determine just one angle, because that would mean that every angle is the same. +1 +1 +1

Add to your Circle Vocab Toolkit... G G Circle: Set of all points the same distance from a fixed point. Named G where G is the center (or the fixed point) radius: Distance from the center to a point on the circle. (r) diameter: Any segment that goes through the center with both endpoints on the circle. (d) Twice the length of the radius FYI:  is not just some random idea! It actually is the result of the ratio . Circumference: “perimeter” or distance around a circle. (C) This is true for ALL circular objects! Area: Region inside the circle. (A)

CS 5 Find: a) The circumference & area of a circle with a diameter of 2.5 in. b) The circumference & area of a circle with a radius of 6 in. c) The diameter of a circle with a circumference of 21 in. d) The radius of a circular pond with a circumference of 31.4 m.

Add to your Circle Vocab Toolkit... Central Angle:  with vertex at center of circle. B Arc: A piece of the circle A Minor Arc: Shorter arc formed by an angle (named with 2 letters) Measure always < 180º! Major Arc: Longer arc formed by an angle (named with 3 letters) Measure always > 180º!

Add to your Circle Vocab Toolkit... 5 cm 60 B Arc Measure: A Number of degrees in the arc Arc measure = central  If mAOB = 60 & the radius of O is 5 cm, find the arc measure. Example: m = m AOB (Arc measure = central ) m = 60

a) State some real-life examples of an arc. CS 11 a) State some real-life examples of an arc. Piece of a bike tire between two spokes, leftover crust from a piece of pizza, edge of a broken plate, etc… b) Sketch an arc that is ¼ of a circle. c) Why do you think that the measure of the arc is the same as the measure of the central angle? The number of degrees in an angle is the same no matter how long or short the sides of the angle are. 60 60

(arc measure = central ) CS 12 F E B Use the figures at the right to answer the following questions. O is the center of each circle. A 120 90 O O G C a) How many degrees are needed for an arc to go completely around a circle? Circle = 360 b) What is the measure of the minor arc ? What is the measure of the major arc ? (circle = 360) m + m = 360 m = m AOB (arc measure = central ) m + 120 = 360 m = 120 m = 240 d) What is the measure of ? m = m EOF (arc measure = central ) c) What is the mEOF? m = 90 mEOF= 90 m + m = 360 (circle = 360) m + 90 = 360 m = 270

Since a circle measures 360… A circle is divided into “n” congruent arcs. What is the measure of each arc if: CS 14 Since a circle measures 360… a) n = 4 ? b) n = 27 ? (circle = 360) (circle = 360) =90 13.33 c) n = 100 ? d) n is any positive integer? (circle = 360) (circle = 360) =3.6

> > > > > > > > For each circle, the vertex of the angle is at the center. Find the measure of x for each. CS 15 a) b) c) x x x 57 57 57 > > d) e) f) m1 = m2 > > 62 x > > x 1 280 > 270 > x 2

This is a new justification! CS 15 a) b) c) x x x 57 57 57 x = 57 Arc measure = central  This is a new justification! x = 57 Arc measure = central  x = 57 Arc measure = central 

Adjacent s that form a straight  CS 15 > > d) e) f) m1 = m2 > > 62 x > > 280 x 1 > 270 > x 2 Arc measure = central  x = 280 x + 270 = 360 (circle = 360) Arc measure = central  = 90 Arc measure = central  m1= m2 = 62 Adjacent s that form a straight  m1 + m2 + x = 180 substitution 2(62) + x = 180 x = 56

Work on the worksheet & MCFR #1-10!