Math problem help on indirect proof

"Write an indirect proof of the following statement: If PQRS is a quadrilateral, then angle Q, angle R, and angle S are not all 120 degrees."

I get how the problem, but I don't know how to explain it. How do I write an indirect proof for it?

In an indirect proof, you must negate the conjecture.

The negation of
If PQRS is a quadrilateral, then angle Q, angle R, and angle S are not all 120 degrees
is
PQRS is a quadrilateral AND Q, R, and S are all 120 degrees.

Now you must find a contradiction. Just by eyeballing this, I can see that the angle sum of the quadrilateral is 360 + m

Probably the best way to do this is by dividing the quadrilateral into 2 triangles by drawing a diagonal through the interior of the quadrilateral.
This divides the quadrilateral into 2 triangles. Note that the angle sums of both triangles, when added together equal the angle sum of the quadrilateral. Then the angle sum of the quadrilateral must be <= 360 by the Saccheri-Legendre Theorem (Angle sum of triangle is <= 180)

Since the sum of the 3 angles in the quadrilateral = 360, the measure of the 4th must be 0 which means that there cannot be a quadrilateral.

Therefore the negation of the original statement is false, or the original statement is true. :)

Suppose that m(Q) = m(R) = m(S) = 120º.
Then the sum of all three angle measures is 360º. m(P), then, must be 0º. However, if this is the case, then PQRS is not a quadrilateral. Therefore, angles Q, R, and S cannot all be 120º.