Given a∥b , and c is not parallel to a or b, which statements must be true? select each correct answer. m∠7=m∠10 m∠4=m∠8 m∠8=m∠9 m∠2=m∠7 brainliest if correct!

The figure consists of three horizontally oriented lines, two of which are

parallel, having a common transversal.

Reasons:

First option;

m∠7 and m∠10 are alternate interior angles

Given the line c is not parallel to line b, we have;

b ∦ c

Therefore;

m∠7 ≠ m∠10 by the inverse of the alternate interior angles theorem

Therefore;

m∠7 = m∠10 is False

Second option;

m∠4 and m∠8 are corresponding angles formed between line a and line b.

Given the line a is parallel to line b, we have;

m∠4 ≅ m∠8 by corresponding angles theorem

Third option;

m∠8 and m∠9 are alternate interior angles formed between non parallel lines

Therefore;

m∠8 ≠ m∠9

Which gives;

m∠8 = m∠9 is false

Option four;

m∠2 and m∠7 are alternate exterior angles, therefore;

m∠2 ≅ m∠7 by alternate exterior angles theorem

The statements that must be true are;

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2.

4.

Step by step explanation:

We have been given that a∥b , and c is neither parallel to a nor b.

Let us see our options one by one to see which is true.

1. m∠7=m∠10

Since we know that alternate interior angles formed by two parallel lines and transversal are congruent.

We can see that ∠7 and ∠10 are on the opposite sides of transversal. In order to have these angles equal lines b and c must be parallel. But we have been given that line c is not parallel to line b. Therefore, and 1st statement is not true.

2. m∠4=m∠8

Since we know that corresponding angles formed by two parallel lines and transversal are congruent.

We can see that ∠4 and ∠8 are formed by our parallel lines a and b and ∠4 corresponds to angle ∠8. Therefore, by corresponding angles postulate and our 2nd statement is true.

3. m∠8=m∠9

We can see that ∠8 and ∠9 are on the opposite sides of transversal. In order to have these angles equal lines b and c must be parallel. But we are told that line c is not parallel to line b. Therefore, and 3rd statement is not true.

4. m∠2=m∠7

Since we know that alternate exterior angles formed by two parallel lines and transversal are congruent.

We can see that ∠2 and ∠7 are on the opposite sides of our transversal and we are given that line a is parallel to line b. Therefore, by alternate exterior angles theorem and 4th statement is true indeed.