I cannot figure out this problem - can anyone break it down for me, please? Correct answer is D.
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Quick high school maths refresher -
Sum of all angles of a triangle equals 180 degrees. -------- (A)
Supplementary angles on a line sum to 180 degrees. ------ (B)
Now in the question above, We need PRS - PQR,
Statement 1:
QPR = 30
From A above - QPR + PQR + PRQ = 180
This implies PQR + PRQ = 150
or, PRQ = 180 - PQR ---------(C)
Also PRQ and PRS are supplementary. So from B above, PRQ + PRS = 180
Substituting for PRQ from C, 180 - PQR + PRS = 150
or, PRS - PQR = 30.
Thus 1 is sufficient.
Statement 2:
PQR + PRQ = 150
or, PRQ = 180 - PQR ---------(D)
Also PRQ and PRS are supplementary. So from B above, PRQ + PRS = 180
Substituting for PRQ from C, 180 - PQR + PRS = 150
or, PRS - PQR = 30.
Thus 2 is sufficient.
Since both statements alone are sufficient, answer is D.
