The measure of angle PRS is how many degrees greater than the measure of angle PQR ? GMAT data sufficiency

It is asked in the question - \(\Lambda{PRS} - \Lambda{PQR}\) = ?
Statement 1: the measure of angle QPR is 30

QPR = 30
In triangle QPR, three angles sum = 180° = \(\Lambda{QPR} + \Lambda{PQR} + \Lambda{PRQ}\)

\(180=30+\Lambda{PQR}+(180-\Lambda{PRS})\)
30 = \(\Lambda{PRS}-\Lambda{PQR}\)

Hence, it is sufficient to get the answer.

Statement 2:
The sum of the angles \(\Lambda{PQR}\) and \(\Lambda{PRQ}\) is 150
Basically, the same information is given \(\Lambda{PQR}+\Lambda{PRQ}\) = 150
\(\Lambda{PQR}\) + 180 -\(\Lambda{PRS}\) = 150
30 =\(\Lambda{PRS}\) - \(\Lambda{PQR}\)
This is also sufficient to get the answer.

Hence, D is the correct answer.

First off, we can deduce from the diagram that (angle SPR) + (angle PRS) + 90 = 180, or (angle SPR) + (angle PRS) = 90.
Since (angle SPQ) + (angle PQR) = 90 in triangle PQS, we know that (angle SPQ) + (angle SQR) + 90 = 180.

Equalize those two:
Angles SPR plus PRS equal angles SPQ plus PQR.
The angles SPQ and SPR are equal to the angles PRS and PQR.

The query is: "The measure of angle PRS is how many degrees greater than the measure of angle PQR?" They are requesting (angle PRS) - (angle PQR), or to put it another way, according to the equation above: if we know (angle SPQ) - (angle SPR), then we also know (angle PRS) - (angle PQR).
First claim: (angle QPR) equals 30 degrees

Since the two little angles that make up the great angle (angle SPQ) are identical, we may deduce that (angle SPQ) = (angle SPR) + (angle QPR).
Consequently, (angle SPQ) = (angle SPR) + 30 – Angles SPQ minus SPR equal 30. Angle PRS minus Angle PQR equals 30.

Statement 1 is adequate on its own.
Secondly, (angle PQR) plus (angle PRQ) equals 150 degrees.
Triangle PQR teaches us that: Angles PQR, PRQ, and QPR added together equal 180 degrees.
Statement 2 is sufficient on its own if (angle PQR) + (angle PRQ) = 150 degrees, as 150 + (angle QPR) = 180 degrees ---> (angle QPR) = 30, and we have the same information as in statement 1.

The amount by which the measure of angle PRS exceeds the measure of angle PQR must be determined.

Statement 1:
Angle QPR is measured at 30°.

Let x be the RPS measurement. The triangle PQS's two interior angles are then 90 and 30 + x. Thus, 180 - (90 + 30 + x) = 180 - 120 - x = 60 - x is the third internal angle of the same triangle. The angle PQS therefore equals 60 - x in terms of x.
Check out the triangular PRS now. The third interior angle (angle PRS) is 180 - (90 + x) = 90 - x because this triangle has two interior angles that are 90 and x.

We may calculate that the angle PRS is greater than the angle PQS by 90 - x - (60 - x) = 90 - x - 60 + x = 30 degrees using the two formulas.
The first claim is adequate to respond to the question.

Statement 2:
The sum of PQR and PRQ's measurements is 150°.
Thus, angle QPR is defined as 180 – 150, or 30°. We can use QPR = 30 to calculate the difference between the measures of angles PRS and PQR using the same method as in statement one.
The second claim is adequate to respond to the question.