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15. Drag and drop an answer to each box to correctly complete the proof.

Given: m∥nm∥n , m∠1=65∘m∠1=65∘ , m∠2=60∘m∠2=60∘ , and BD−→−BD→ bisects ∠ABC∠ABC .

Prove: m∠6=70∘

 

https://static.k12.com/nextgen_media/assets/8124235-NG_GMT_SemA_ST_Pt1_DP002_570_002.png

 

It is given that m∥nm∥n , m∠1=65∘m∠1=65∘ , m∠2=60∘m∠2=60∘ , and BD−→−BD→ bisects ∠ABC∠ABC . Because of the triangle sum theorem,  m∠3=55∘m∠3=55∘ . By the_____It is given that m∥nm∥n , m∠1=65∘m∠1=65∘ , m∠2=60∘m∠2=60∘ , and BD−→−BD→ bisects ∠ABC∠ABC . Because of the triangle sum theorem,  m∠3=55∘m∠3=55∘ . By the_____, m∠ABC=110∘m∠ABC=110∘ . m∠5=110∘m∠5=110∘ because vertical angles are congruent. Because of the_____, m∠5+m∠6=180∘m∠5+m∠6=180∘ . Substituting gives110∘+m∠6=180∘110∘+m∠6=180∘ . So, by the_____m∠6=70∘m∠6=70∘ .

 

ANSWER CHOICES

.

linear pair postulate

definition of bisector

transitive property of equality

angle addition postulate

same-side interior angles theorem

corresponding angles postulate

alternate interior angles postulate

subtraction property of equality

 Jan 18, 2018

Best Answer 

 #1
avatar+7352 
+1

 

It is given that m || n , m∠1 = 65° , m∠2 = 60° , and BD bisects ∠ABC .

 

Because of the triangle sum theorem,  m∠3 = 55°.

 

By the definition of bisector, m∠ABC = 110°. (unsure of this one, but no other choice seems right)

 

m∠5 = 110° because vertical angles are congruent.

 

Because of the same-side interior angles theorem, m∠5 + m∠6 = 180°.

 

Substituting gives 110° + m∠6 = 180° .

 

So, by the subtraction property of equality, m∠6 = 70°

 Jan 18, 2018
 #1
avatar+7352 
+1
Best Answer

 

It is given that m || n , m∠1 = 65° , m∠2 = 60° , and BD bisects ∠ABC .

 

Because of the triangle sum theorem,  m∠3 = 55°.

 

By the definition of bisector, m∠ABC = 110°. (unsure of this one, but no other choice seems right)

 

m∠5 = 110° because vertical angles are congruent.

 

Because of the same-side interior angles theorem, m∠5 + m∠6 = 180°.

 

Substituting gives 110° + m∠6 = 180° .

 

So, by the subtraction property of equality, m∠6 = 70°

hectictar Jan 18, 2018

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