Respuesta :
Answer:
2. [tex]m\angle4=m\angle8[/tex]
4.[tex]m\angle2=m\angle7[/tex]
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, [tex]m\angle7\neq m\angle10[/tex] 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 [tex]m\angle4=m\angle8[/tex] 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, [tex]m\angle8\neq m\angle9[/tex] 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 [tex]m\angle2=m\angle7[/tex] and 4th statement is true indeed.
The figure consists of three horizontally oriented lines, two of which are
parallel, having a common transversal.
- The true statements are; m∠4 = m∠8 and m∠2 = m∠7
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
- m∠4 = m∠8 is true by definition of congruency
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
- m∠2 = m∠7 is true, by definition of congruency
The statements that must be true are;
- m∠4 = m∠8 and m∠2 = m∠7
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