Question

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∘

Line m parallel to line n. Line t passing through both lines. There are four angles formed by lines m and t intersecting at point B. The lower left angle is labeled 5. The upper right angle is angle A B C with point A on line t and point C on line m. Angle A B C is separated by ray B D. The angle on the right side of the ray is labeled 4. The angle on the left side is labeled 3. A segment joins points A and D forming a triangle with angle 3 as one of its interior angles. The other two interior angles are labeled 1 and 2. There are four angles formed by lines n and t intersecting. The upper left angle is labeled 6.

Put responses in the correct response input area to answer the question. Select a response, navigate to the desired input area and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
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 Press enter key to drop response here.Response input area, ∠3≅∠4
, so m∠4=55∘
. Using the Press enter key to drop response here.Response input area, m∠ABC=110∘
. m∠5=110∘
because vertical angles are congruent. Because of the Press enter key to drop response here.Response input area, m∠5+m∠6=180∘
. Substituting gives 110∘+m∠6=180∘
. So, by the Press enter key to drop response here.Response input area, m∠6=70∘
.

Answer 1

1) BD bisects ∠ABC (definition of angle bisector)
2) Angle Addition Postulate (m∠ABC = m∠3 + m∠4)
3) Same-side (consecutive) interior angles are supplementary (for parallel lines)
4) Subtraction Property of Equality (subtract 110° from both sides)