Question

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

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 (_________)?, ∠3≅∠4 , so m∠4=55∘ . Using the (_________)?, m∠ABC=110∘ . m∠5=110∘ because vertical angles are congruent. Because of the (_________)?, m∠5+m∠6=180∘ . Substituting gives 110∘+m∠6=180∘ . So, by the (________)?, m∠6=70∘ .

Answer 1

Explanation:

Answer 2

1. Angle Bisector Theorem
2. Sum of Adjacent Angles
3. Co-interior angle property
4. Additive law

Explanation:

Note: Diagram for Question is attached

1. Angle Bisector Theorem

BD is the angle bisector. Bisection means dividing in 2 equal parts. So angle 3 and angle 4 are equal.

2. Sum of Adjacent Angles

Two adjacent angles can be added together to find the larger angle that is formed by the two angles.

3. Co-interior angle property

Co-interior property states that if a single line intersects two parallel lines, the sum of interior angles (of same side) is equal to 180. (Image attached for visual representation)

4. Additive law

By additive law, we can subtract a value from both sides of the equation without unbalancing the equation. So, we can subtract 110 from both sides of the equation giving 70 as the final answer.