Help help help please really need help If AC ll BD and M<6 and is doubled, how must M<3 be changed to keep the lines parallel?

A. M<3 would stay the same.

B. M<3 would need to double.

C. M<3 would need to be cut in half.

D. The answer cannot be determined.

- Based on the given information, determine which sides of quadrilateral ABCD must be parallel.

M< A= 72 degrees, M< B=108 degrees, M< C= 72 degrees, M< D=108 degrees

A. AB ll DC

B. AD ll BC

C. AB ll DC and AD ll BC

D. none of these sides must be parallel

Problem 1

Explanation: This is because angles 3 and 6 are congruent corresponding angles. Corresponding angles are congruent whenever we have parallel lines like this. If they weren't congruent, then the lines wouldn't be parallel. We would need to double angle 3 to keep up with angle 6.

Problem 2

Explanation: We have angles A and C that are same side interior angles, but they add to A+C = 72+72 = 144, which is not 180. The same side interior angles must add to 180 degrees for parallel lines to form. This shows AB is not parallel to CD.

A similar situation happens with angles B and D, since B+D = 108+108 = 216. This also shows AB is not parallel to CD. We can rule out choices A and C.

Choice B is false because AD is a diagonal along with BC. The diagonals of any quadrilateral are never parallel as they intersect inside the quadrilateral. Parallel lines never intersect.

The only thing left is choice D. We would say that AC || BD, since A+B = 72+108 = 180 and C+D = 72+108 = 180, but this isn't listed as an answer choice.

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step-by-step explanation:

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