Unit 9 Lesson 2 Find Arc Measures And

Unit 9 Lesson 2 – Find Arc Measures And Use Inscribed Angles and Polygons

Term Definition Picture A C Central Angle An angle whose vertex is the center of the circle P

Term Definition Picture A C Minor Arc of a circle that is less than 180° P Two letters:

Term Definition Picture A C Major Arc of a circle that is more than 180° P B 3 letters:

Term Definition Picture A Semicircle Arc of a circle that is 180° P B C 3 letters:

Term Congruent circles Definition Two circles with the same radius Picture

Term Congruent arcs Definition Arcs that have the same central angle Picture A B D C

The measure of a minor arc is the central measure of its _______ angle. A x° x° P C

73° minor 73°

107° minor 73° 26°

154° minor 73° 26°

206° major 73° 107° 26°

81° minor 73° 107° 26°

180° semicircle 73° 107° 26°

180° Semicircle 73° 107° 26°

287° major 73° 107° 26°

10. 4 – Use Inscribed Angles and Polygons

Inscribed angle: An angle whose vertex is on a circle and whose sides are chords of the circle

Intercepted Arc: An arc that is inside an inscribed angle

Inscribed Polygon : A polygon that has all of its vertices on a circle

Circumscribed Circle: The circle that contains the vertices of a polygon

half The measures of an inscribed angle is ____ the measure of its _______ arc. intercepted 2 x° x° D = AB 2

intercept If two inscribed angles of a circle _______ the same arc, then the angles are _______. congruent D C

A ____ right triangle is inscribed in a circle iff the ________ is a diameter of the circle. hypotenuse B is a right angle because it inscribes a semicircle.

quadrilateral A __________ can be inscribed in a circle iff its opposite angles are _______. supplementary m D + m F = 180° m E + m G = 180°

Find the indicated measure. 158 = = 79° 2

Find the indicated measure. 180 = = 90° 2 90° 180°

Find the indicated measure. = 40 2 = 80°

Find the indicated measure. 88° 92 = = 46° 2

Find the indicated measure. 80 = = 40° 2 100° 80°

Find the indicated measure. 56 = = 28° 2 56°

Find the measure of A and C. 80 m A = = 40° 2 64° 80° 64 m C = = 32° 2

Find the measure of A and C. 146° 146 m A = = 73° 2 62 m C = = 31° 2 62°

68 m PNO = 2 = 34°

62 m QNP = 2 = 31° 62°

= 130° 62°

= 112° 62°

= 248° 112° 62°

Decide whether a circle can be circumscribed about the figure. No, 70 + 130 180

Decide whether a circle can be circumscribed about the figure. Yes, 91 + 89 = 180 91°

Decide whether a circle can be circumscribed about the figure. No, 115 + 63 180

Find the value of the variables. 5 x + 110 = 180 5 x = 70 x = 14° 2 y + 104 = 180 2 y = 76 y = 38°

Find the value of the variables. x + 108 = 180 y + y = 180 x = 72° 2 y = 180 y = 90°

Find the value of the variables. 44° 4 x = 84+44 1 2 7 y = 152+44 1 2 8 x = 128 14 y = 196 x = 16° y = 14°

Find the value of the variables. 171° 12 x = 96+48 1 2 24 x = 144 x = 6° 3 y = 48+171 1 2 6 y = 219 y = 36. 5°

HW Problem Lesson 2 3 -12, 16, 17, 22, 23 Homework 3 -8, 11 -15 odd, 16 #15 66° 3 a = 54+66 1 2 6 a = 120 a = 20° 4 b = 66+110 1 2 8 b = 176 b = 22°