Inscribed Angles 9.4.

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Presentation transcript:

Inscribed Angles 9.4

Warm Up Find each value. 1. mBCA 2. t Solve for x. 3. 58 – x = 4 (x + 7) 4. 2 (x – 8) = 8

An inscribed angle has its vertex ON the circle and its sides are chords of the circle.

m∠ACB = ½ measure of arc AB The measure of an inscribed angle is equal to half the measure of the arc. m∠ACB = ½ measure of arc AB 60 40

If mAB=60 degrees. Is AX = XB? Is AC = BC? Find ACB. Find mACB. Find mAXB.

An angle formed by a chord and a tangent is also equal to the half the arc that is created. m∠1 = ½ measure of arc AB In Circle C, what is m∠ABC?

Central Inscribed Angle Angle

Find x

If KN = 50, then m1= 2. If MN = 110, then m2= 3. If KN = 70 and MN = 115, then KNM= 4. If KPM = 170 and KP = 100, then PM= 5. If m 1 = 28, then KN= 6. If m 2=76, then NM = 7. If m 1 = 24 and m 2 = 68, Then KNM= 8. If m 1 = 28 and m 2 = 69, then KPM=

If two inscribed angles intercept the same or congruent arcs, then the angles are congruent. 68 ̊

Find AB A B B A

Find mEDF.

Find x

Find x

Find a.

Find z.

In circle P, EN=66, m∠GPM=89 ̊, GN is a diameter. GM b. NM c. GE d. m  GEN e. m  EGN f. m  EMN g. m  GNM h. m  GME i. m  EGM

In Circle Z, AB // DC, BC = 94 ̊̊ and m∠AZB = 104 ̊. mBAC mADB

Find each measure. mDAE

Find the angle measures of GHJK.

Find the angle measures of JKLM.

Lesson Quiz: Part I Find each measure. 1. RUS 2. a 3. Find the angle measures of ABCD.