Angle Bisector Missing Angles

The figure is an example of a(n) ...

• angle bisector

• perpendicular bisector

• median

• midsegment

Find the missing angle.  Find x.

• 20^o

• 70^o

• 160^o

• 180^o

Find the m∠1

• 67

• 113

• 180

• 23

Find the m<WYZ.

• 9°

• 18°

• 36°

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

What is the missing statement in the proof?

• 2m∠ABD = m∠ABD + m∠ABD

• m∠ABD = m∠DBC

• m∠ABC = m∠ABC

• m∠ABD +m∠ABD = m∠ABD + m∠DBC

Q1. What is the value of x?

• A) x=67

• B) x=43

• C) x=55

• D) x=12

What is the missing statement in the proof?

• 2m∠ABD=m∠ABD+m∠ABD

• m∠ABD=m∠DBC

• m∠ABC=m∠ABC

• m∠ABD+m∠ABD=m∠ABD+m∠DBC

The figure shows a triangle with one of its bisectors.

• 112

• 38

• 97

• 86

Which of the following below would fill in the Reasons in the proper order?

• Given; Definition of bisect; Transitive; Given, Definition of bisect

• Given; Transitive; Given; Definition of bisect; Definition of bisect

• Given; Definition of bisect; Given; Definition of bisect; Transitive