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In the figure above m1 is parallel to m2, and n1 is...

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In the figure above m1 is parallel to m2, and n1 is...

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In the figure above m1 is parallel to m2, and n1 is parallel to n2. The degree measure of which of the following angles is NOT necessarily equal to the degree measure of angle S?

(A) P
(B) Q
(C) R
(D) T
(E) V

The OA is E.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

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swerve wrote:

In the figure above m1 is parallel to m2, and n1 is parallel to n2. The degree measure of which of the following angles is NOT necessarily equal to the degree measure of angle S?

(A) P
(B) Q
(C) R
(D) T
(E) V

The OA is E.

Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
Hi Swerve,
Let's take a look at your question.

In the image, m1 is parallel to m2, and n1 is parallel to n2.
We need to find the degree measure of which of the angles given in the options is NOT necessarily equal to the degree measure of angle S.

Let's start with Option A.
The degree measure of S is equal to the degree measure of P.
Because,
Angle S = Angle T (Corresponding angles)
Angle T = Angle Q (Corresponding angles)
Angle Q = Angle P (Vertical angles)
Therefore,
Angle S = Angle P
Hence, Option A is not correct.

OPTION B:
Let's check if Angle S is equal to Angle Q.
Angle S = Angle T (Corresponding angles)
Angle T = Angle Q (Corresponding angles)
Therefore,
Angle S = Angle Q
Hence, Option B is not correct.

OPTION C:
Let's check if Angle S is equal to Angle R.
Angle S = Angle R (Corresponding angles)
Hence, Option C is not correct.

OPTION D:
Let's check if Angle S is equal to Angle T.
Angle S = Angle T (Corresponding angles)
Hence, Option D is not correct.

OPTION E:
Let's check if Angle S is equal to Angle V.
If we look closely inside the triangle, whose one of the angles is S, we can see that the other angle of this triangle and V are vertical angles, so they are congruent.
It means Angle S is not equal to V.
Hence, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
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