Inscribed Angles

Inscribed Angles

9.4

Warm UpFind each value.

1. mBCA

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.

• 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.

1.Is AX = XB?

2.Is AC = BC?

3.Find ACB.

4.Find mACB.

5.Find mAXB.

• 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 InscribedAngle Angle

Find x

1. If KN = 50, then m1=

2. If MN = 110, then m2=

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 BA B

Find mEDF.

Find x

Find x

Find a.

Find z.

In circle P, EN=66, m∠GPM=89 ̊, GN is a diameter.

a. 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 ̊.

a.AB

b.mBAC

c.mADB

Find each measure.

mDAE

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.