CPM Homework Help : GC Problem 12-56

Triangle P, Q, R, is drawn with an interior point, S. Segments P, S, and S, R, are drawn. Angle S, P Q, is 40 degrees. Angle S, R, Q, is 35 degrees, and angle P, S, R, is 140 degrees. In $\Delta PQR$ at right, what is $m\angle Q$ ? Explain how you found your answer.

Note:

There are multiple ways to find the measure of $\angle Q$ .

One Method:

Examine the quadrilateral $PQRS$ . The sum of the interior angles should be $360^\circ$ .

Reminder:

Check your answer! Is your answer for $m\angle Q$ $\Delta PQR$ and $\Delta PSR$ possible?