Question

Given a∥b, and c is not parallel to a or b, which statements must be true? Responses m∠8=m∠9 StartFragment, m∠8=m StartFragment ∠9, m∠7=m∠10 StartFragment, m∠7=m∠10, m∠2=m∠7 StartFragment, StartFragment, m∠2=m∠7, ,

Answer 1

So, the statement that must be true is:

m∠7 = m∠10

Explanation:

The given information is that line a is parallel to line b, and line c is not parallel to either a or b. From this, we can make the following conclusions:

1. m∠8 = m∠9: This statement is not necessarily true just based on the given information. We don't have enough information to conclude that these angles are equal.

2. m∠7 = m∠10: This statement is true. When a transversal intersects two parallel lines (a and b), the alternate interior angles are congruent, so m∠7 is congruent to m∠10.

3. m∠2 = m∠7: This statement is not necessarily true based on the given information. We don't have enough information to conclude that these angles are equal.

So, the statement that must be true is:

m∠7 = m∠10