SAT Mathematics Practice Test 5

The measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc. That is,$\mathit{m}\mathit{D}\mathit{A}=\frac{\mathit{x}°}{2}$ Also, the sum of the interior angles of quadrilateral ABCP is $360°$, and the measure of the obtuse angle P is $360°-\mathit{x}°$.Hence,.simplifying this equation gives $\frac{\mathit{x}°}{2}=40°$, and so $\mathit{x}=80$
Alternate approach: If points A and P are joined, then the triangles that will be formed, APB and APC, are isosceles because$\mathit{P}\mathit{A}=\mathit{P}\mathit{B}=\mathit{P}\mathit{C}.$ It follows that the base angles on both triangles each have measure of $20°$. Angle A consists of two base angles, and therefore,$\mathit{m}\angle \mathit{A}=40°$.Since the measure of an angle inscribed in a circle is half the measure of the central angle that intercepts the same arc, it follows that the value of $\mathit{x}$ is $80°$.