Angle Addition and Angle Bisectors

• x=67
• x=43
• x=55
• x=12

• m<EFJ = 90, m<JFG = 90

• m<EFJ = 45 m<JFG = 45

• m<EFJ = 180, m<JFG = 180

• m<EFJ = 45 m<JFG = 90

What is the value of x?

• 10.667

• 11.333

• 42

• 10

Calculate m∠ABC.

• 45°

• 60°

• 105°

• 15°

• A
• B
• C
• D

Angle JHG measures 161.

• m∠GHK=80.5,

  m∠KHJ=161

• m∠GHK=161,

  m∠KHJ=80.5

• m∠GHK=80.5,

  m∠KHJ=80.5

• m∠GHK=161,

  m∠KHJ=161

Given: m∠LAN = 30⁰ , m∠1 = 15⁰
Prove: AM bisects ∠LAN
Step 1: m∠LAN = 30⁰ 
Step 2: m∠1 + m∠2 = m∠LAN
Step 3: m∠1 + m∠2 = 30⁰
Step 4: m∠1 = 15⁰
Step 5: 15⁰ + m∠2 = 30⁰
Step 6: m∠2 = 15⁰
What is the justification for Step 6?

• Subtraction property of equality

• Substitution

• Addition property of equality

• Definition of congruent angles

Given: m∠LAN = 30⁰ , m∠1 = 15⁰
Prove: AM bisects ∠LAN
Step 1: m∠LAN = 30⁰ 
Step 2: m∠1 + m∠2 = m∠LAN
Step 3: m∠1 + m∠2 = 30⁰
Step 4: m∠1 = 15⁰
Step 5: 15⁰ + m∠2 = 30⁰
Step 6: m∠2 = 15⁰
Step 7: m∠1 = m∠2
Step 8: ∠1 ≅ ∠2
Step 9: AM bisects ∠LAN
What is the justification for Step 9?

• Symmetric property of congruence

• Definition of angle bisector

• Addition property of equality

• Definition of congruent angles

Challenge problem: Segment DP is an angle bisector

• 12.5

• 25

• 75

• 50

Given: m∠LAN = 30⁰ , m∠1 = 15⁰
Prove: AM bisects ∠LAN
Step 1: m∠LAN = 30⁰ 
Step 2: m∠1 + m∠2 = m∠LAN
Step 3: m∠1 + m∠2 = 30⁰
Step 4: m∠1 = 15⁰
Step 5: 15⁰ + m∠2 = 30⁰
Step 6: m∠2 = 15⁰
Step 7: m∠1 = m∠2
What is the justification for Step 7?

• Subtraction property of equality

• Transitive property of equality

• Addition property of equality

• Definition of congruent angles