Question

Given that lines a and b are parallel, what angles formed on line a when cut by the transversal are congruent with ∠7?

Answer 1

Answer:

∠2 and ∠3

Step-by-step explanation:

Given:

lines a and line b are parallel and cut by transversal.

We need to find the which angles from line a are congruent to ∠7

Solution:

Now we know that;

line a║line b , So by corresponding angle postulate which states that;

"When two parallel lines are cut by a transversal , the resulting corresponding angles are congruent."

so  we can say that;

∠2 ≅ ∠6

Also by Vertical angle theorem which states that;

"If two angles are  vertical angles, then they are congruent ."

so  we can say that;

∠2 ≅ ∠3    and  ∠6 ≅ ∠7

So by Transitive Property of Congruence which states that;

When $a \cong b\ \ \ and \ \ \ b\cong c \ \ \ so \ \ \ a\cong c$

so  we can say that;

∠2 ≅ ∠3 ≅ ∠6 ≅ ∠7

Hence measure ∠2 and ∠3 are congruent to measure ∠7.