Page 167 - Math Course 3 (Book 2)

Inscribed Angles

So, mYZ = 96 and mUW = 96 3. ∠GEF intercepts GF; 3. Definition of
∠QPR intercepts QR intercepted arc
1
m∠1 = mUW
2 4. ∠GEF ≅ ∠QPR 4. Inscribed angles of ≅
1 m∠2 + m∠3 + m∠4 = 180 arcs are ≅.
= (96) or 48
2 20 + 54 + m∠4 = 180 5. ∠PJK ≅ ∠EHG 5. Right angles are
1 m∠4 = 106 congruent.
m∠2 = mXY
2 6. △PJK ≅ △EHG 6. AAS
1
= (40) or 20
2 1
m∠5 = mUZ
1 2
m∠3 = mUZ 1 Your Turn!
2 = (108) or 54
2
1
= (108) or 54 Measures of Incribed Angles
2

X
m∠1 = 48; m∠2 = 20; m∠3 = 54;
Answer
m∠4 = 106; m∠5 = 54;
2 3

W 1
Proof with Inscribed Angles 5 Y

Example A

Given: ⊙C with QR ≅ GF and JK ≅ HG 4
Prove: ΔPJK ≅ ΔEHG
Z
Q
In ⊙A, mXY = 60, mYZ = 80, and mWX = mWZ. Find
K the measures of the numbered angles.
Find m∠1. Find m∠2.
P J A. 30 A. 110
R B. 60 B. 55
C C. 15 C. 125
H D. 120 D. 27.5
E F
Answer Answer

G

Proof:
Statements Reasons

1. QR ≅ GF and JK ≅ HG 1. Given

2. If 2 chords are ≅ ,
2. QR ≅ GF corr. minor arcs
are ≅.

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