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Question

narissa · Answer

@steve816

narissa · Answer

C?

tteesstt8080 · Answer

Give your explanation for why you think it is C. After all, we can use the process of elimination, too.

tteesstt8080 · Answer

Remember, a straight line is 180 degrees.

will.h · Answer

It is A 
Alternatate exterior angleS of parallel lines  cut by transversal are congruent

mathstudent55 · Answer

@narissa Ignore the answer given above.
It's better for you to go through each option and see why or why not it applies.

mathstudent55 · Answer

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will.h · Answer

Mathstudent it is a postulate so stop the pretence

mathstudent55 · Answer

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mathstudent55 · Answer

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mathstudent55 · Answer

Angles 1, 2, 3, and 4 are called "exterior angles" because they are "outside" the parallel lines.

narissa · Answer

I thought it was C because I thought they where all supplementary angles. Didn't they any of them looked congruent. But I guess I was wrong..

tteesstt8080 · Answer

mathstudent is correct

mathstudent55 · Answer

Angles 1 and 4 are "alternate exterior angles"
Angles 2 and 3 are "alternate interior angles"
The "alternate part refers to the angles being on different sides of the transversal.

mathstudent55 · Answer

In your problem, each drawing shows a pair of alternate exterior angles.
In the one case, they both measure 160 deg.
In another case, they both measure 123 deg.
In the third case, they both measure 45 deg.

mathstudent55 · Answer

@narissa Do you understand so far?

mathstudent55 · Answer

Notice that in each case, the two angles are indeed alternate exterior angles.
What do you notice is the relationship between the to angles in each case?

narissa · Answer

oh yes thank you : )

mathstudent55 · Answer

Notice that in each case, the two alternate exterior angles have the same measure, so they are congruent.

mathstudent55 · Answer

That makes option A true.

mathstudent55 · Answer

Now look at option B.
The 45-deg angles are not obtuse.
Also, in the cases of the 160-deg angle and the 123-deg angle, there are also alternate exterior angles of 20 deg and 57 deg which are not obtuse.
This makes option B not always true.

mathstudent55 · Answer

Look at option C.
In the case where the two alternate exterior angles measure 160 deg, they are clearly not supplementary because the sum of 160 and 160 is not 180.

mathstudent55 · Answer

With option D, again, keep in mind that since one angle in one pair of alternate exterior angles measures 160 deg, then the other angle in the pair measures 20 deg, so not all angles formed are congruent.

mathstudent55 · Answer

The only option that is always true is A.