Question

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

Given: m∥n , m∠1=65∘ , m∠2=60∘ , and BD−→− bisects ∠ABC
Prove: m∠6=70∘

Answer 1

1: Definition of bisector

2: Angle addition postulate

3: Same-Side interior angles theorem

4: Subtraction property of equality

Explanation:

I took the test

Answer 2

Definition of bisector

Angle addition postulate

same side interior angles theorem

subtraction property of equality

Explanation:

It is given that m║n, m∠1 = 65°,m∠2=60° and BD --> bisects ∠ABC . Because of triangle sum theorem, m∠3 = 55°. By the definition of bisector , ∠3 ≅∠4, so m∠4= 55°. Using the angle addition postulate , m∠ABC = 110°, m∠5 = 110° because vertical angles are congruent . Because of 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°.