Angle Addition Bisector

• x=67
• x=43
• x=55
• x=12

What is the value of x?

• 10.667

• 11.333

• 42

• 10

Calculate m∠ABC.

• 45°

• 60°

• 105°

• 15°

Angle ABC measures 34^o. What is the measure of angle CBD?

• 17^o

• 34^o

• 68^o

• x=3/17
• x=9
• x=3
• x= -3

Answer explanation

9x=8x+3

• m∠GHK=26, m∠KHJ=26
• m∠GHK=26, m∠KHJ=52
• m∠GHK=52, m∠KHJ=52
• m∠GHK=52, m∠KHJ=26

JHK is 52. Find the measures of angles GHK and GHJ.

• m∠GHK=52, m∠GHJ=104

• m∠GHK=104, m∠GHJ=52

• m∠GHK=26, m∠GHJ=26

• m∠GHK=52, m∠GHJ=26

Answer explanation

"bisects" means that it makes two EQUAL angles, so if one part is 52, then the other part is also 52!

To get the whole, we use angle addition to do 52+52=104

• x=3/17
• x=9
• x=3
• x= -3

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

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