# SAT Math Multiple Choice Question 620: Answer and Explanation

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**Question: 620**

**5.**

Note: Figure not drawn to scale.

In the figure above, *P* is the center of a circle and *AC* is its diameter. What is the value of *x*?

- A. 60
- B. 50
- C. 40
- D. 30

**Correct Answer:** C

**Explanation:**

**C**

**Additional Topics (circles and triangles) MEDIUM**

Since *PA* and *PB* are both radii of the circle, they are congruent, and so triangle *APB* is isosceles. By the Isosceles Triangle Theorem, then, angle *A* must also be 20°. From here, you might simply notice that the angle we're looking for, *CPB*, is the external angle to this triangle, and so it has a measure equal to the sum of the two remote interior angles: 20° + 20° = 40°. Alternately, you could notice that angle *APB* must have a measure of 140° (since all angles in a triangle have a sum of 180°), and since *AC* is a straight line, angle *CPB* = 180° - 140° = 40°.