1 What is the Triangle Exterior Angle Theorem

1) What is the Triangle Exterior Angle Theorem? 2) Solve for x. 3) Solve for y. R A (5 x)° (2 y - 3)° B Q S C T (y - 1)° D

Secant B A Secant is a line that intersects a circle at two points. F E

Theorem If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is half the sum of the measures of its intercepted arcs. A C Chords AD and BC intersect at E. m<1 = ½ (m. AB +m. CD) 1 B E D

Examples Find each angle measure. 1. Find m<SQR 2. Find m<ABE A S P 65° 32° T E B 100° 37° Q R D 3. Find m. MQ M R 160° Q N P 255° C

You try 4. Find m<AEB A 5. Find m. RS 139° R S 100° D E 113° N B L C 90° 6. Find m<LPO L 65° M T O 80° P N

Theorem If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is half the difference of the measures of its intercepted arcs. Two Tangents Tangent and Secant A B C E F Two Secants K 2 L 1 D m<1 = ½ (m. AD – m. BD) J H G m<2 = ½ (m. EHG – m. EG) 3 M N m<3 = ½ (m. JN – m. KM)

1. Examples 2. R 174° Q 98° x° P S F E x° 132° G 3. 25° L K M J 83° x° N

4. R 5. E 200° 74° S Q 225° x° P 6. x° G J x° N K 25° 30° L M F

Summing Up Angles in Circles Where’s the What’s the Vertex? Angle Measure? Vertex on a circle Examples 200° Half of the arc 120° 1 2 m<1=60° Vertex inside a circle Vertex outside a circle Half of the arcs added Half of the arcs subtracted 44° 1 78° 1 m<2=100° 86° 202° m<1= ½ (202°-78°) = 62° m<1= ½ (44°+86°) = 65° 2 45° 125° m<2= ½ (125°-45°) = 40°

Whiteboards • Practice 12 -4 Workbook P 491 #1 -12 all

Warm Up 1. Find m. AF 2. Find LP A 48° N 80° 160° E 110° B m. LR= 100° M D F L C S R On the white boards! 3. Find m. YZ X 49° Y 113° W 68° P Z Q 26°

Last 4 E 31° 1. m<FGJ 2. m<HJK F G 52° H J 130° K 3. Solve for x 4. m. CE D C 150° B E J A 83° x H 25° G 48°

P 681 # 5 – 24 all, 36 P 691 # 2 -14 even, 20 - 24 even Period 1 Due Tuesday Period 2/4 Due Wednesday Exam on Thurs/Fri