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Secondary 2

HW 12.3 Inscribed Angles

Name___________________________________ ID: 1

Date________________ Period____

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-1-

Find the measure of the arc or angle indicated.

1)

K

L

M

71 °?

2) L

M

N

?

3)

G

F

E

?

57 °

78 °

4)

B

CD

140 °

60 °

?

Solve for x.

5)

C

D

E

K

108 °

7x - 6

6)

PQ

RE

8x - 12

9x - 13

80

Selected solutions

An inscribed angle is formed by 2 chords of a circle

The size of an inscribed angle Is always 42 the size of its intercepted arc

(71×2)=142

1800-780-57=45

hi4514=90

MLEDF =90°because it 5-40+7*-6=90Opens to 48+7×-90

the diameter )54°- 48 -48

me KDC .

.

s4✓25=4,1

108 ÷ 2=540×=6

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-2-

7)

P

Q

R

15x - 5 62 °

76 °

8)

Z

Y

X

39x - 1

136 °

70 °

Find the measure of the arc or angle indicated.

9) Find YWXm

W

X

Y

8x + 6

27x - 4

78 °

10) Find MKLm

K

L

M

2 + 14x

8 + 20x

11) Find mST

R

S T

114x

65x + 1

12) Find mEF

D

E

F

X

4x - 3

2x + 27

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are

tangent.

13) L

KJ

?

55 °

16294=124:

XI+12-4971=36015×+195=360

- 195- 195

1511=165

⇐1=11

3607-8+8×1=6+27×-1 mLYWX=2l2°÷2= =

360=80+3 SXMLY

-80 -80

yMtloq

280=35×3-535

X

:%µ,€y=2H

27 (8) -4

216.4212

61×+1+1141=1800179×+1=180- 1 - 1

180 1791=179(semicircle) 179¥

:5×+1=650+165+1=66

most -660

The size of an angle formed by a tangent line and chord is Yzthe size of its

air5 Mtv

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-3-

Solve for x. Assume that lines which appear tangent are tangent.

14)

U

T

S2 + 9x

55 °

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are

tangent.

15) Find QRSm

S

R

Q

146x - 2

16x + 3

16) Find MLKm

K

L

M

17x + 3

7x + 15

Determine if line AB is tangent to the circle.

17)

15

8

9B

A

18)

18

20

12B

A

Find the segment length indicated. Assume that lines which appear to be tangent are tangent.

19) 8.4

11.6

?

20)

10.2

17

?

.360-2116×+3=146×-2

36-0-32×-6=146×-2-

354-34=146×-2+32×+32×354=178×-2

+2 +2

356=17811

#tFG, × - z

1m<ars=16Xt3mFa=2( 16×+3 ) 1614+3

32 '-3 m< QRS -35

If Arsislangent , st

17 then MLA shouldbe 90

?If MLA -90;

then ...

8 152+82=172

225+64=289

289=2891

tango :42+112=11.62

70.56+1/2=134.56-70.56 - 70.56 ×

E2=64±8

.

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-4-

Find the angle measure indicated. Assume that lines which appear to be tangent are tangent.

21)

79 °

?

22)

49 °

?

Solve for x. Assume that lines which appear to be tangent are tangent.

23)

8x + 5

9x24)

17 + x

-1 + 3x

Find the perimeter of each polygon. Assume that lines which appear to be tangent are tangent.

25)

18.78.9

16.8

16.6

26) 8.5

6.6

19.9

18.4

All Angles in a quadrilateral add up to 360

L

this line is

tangent .suT

this angle must

beg

:60-790-90-900=1

:1=8×5

-8¥1=5

6.8168-6.8=10 6.6-9.8=6.8

-

9.810

18.9gq 1%8%7-8.9=9.8

18.9+18.7+16.6+16.8=71

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-5-

Find the length of the segment indicated. Round your answer to the nearest tenth if necessary.

27)

16.2

12.7

7.9

x

28)

11.2

x13.5

29)

10

x

13.1

Solve for x. Assume that lines which appear to be diameters are actual diameters.

30) 65°

55°

x + 70

raid

fadi-7.9+12.7=12.6

-

Radius -43.1 y2+I0 ?_ 13.12

ratuxf" 92 'iYoooIomou

3.1 $71.615- 8.5

X= 13.1 -8.5=4.6