Data Sufficiency

OA is C can someone explain.

ershovici wrote:OA is C can someone explain.

We all agree that 1 and 2 alone are not sufficient. So A, B and D are out.
Lets test for C. I strongly recommend you draw this as we speak.

First lets mark up some missing angles with variables based on information given to us in 1 and 2.

Angle SUT = Angle STU ( equal sides of triangle SUT) Lets call this angle "a"
Angle RQB = Angle RSQ ( equal sides of triangle RQS) Lets call these angles "b"

Since RST is a straight line, then

a + b + x = pie ....................... Equation 1

Now lets look at quadrilaterlal PQSU.
Sum of all interior angles should be 2 pie.

two of the angles are supplimentary to a and b.

( pie - a ) + (pie - b) + x + pie/2 = 2 pie which simplifies to :

a + b -x = pie/2 .................................. Equation 2

At this point you know the information provided to you was sufficient. Mark your answer and move on. But since we are not in a middle of an exam lets solve it to death.

Lets say a+b is called J the junk variable we dont care about.

Two equations are

J + x = pie ....... New Equation 1
J - x = pie/2 ....... New Equation 2

Solve these simultaneous equations for J you get x = pie/4

P + R + T = 180

R + T = 90 .............................(1)

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Option A)
making a small isosceles triangle on top

R + Q + S1 = 180

R + 2Q = 180

Q or S1 = 90 - R/2 ...................(2)

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Option B)
simliarly

S2 or U = 90 - T/2 ...................(3)

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add (2) and (3)

S1 + S2 = 180 - (R+T)/2

180 - X = 180 - (90)/2

X = 45

Hence, C.