Answer:
(C) [tex]110^{\circ}[/tex].
Step-by-step explanation:
Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle, therefore
[tex]{\angle}FED=90^{\circ}[/tex].
Now, it is given from the figure that [tex]{\angle}FEP=35^{\circ}[/tex], therefore
[tex]{\angle}FED={\angle}FEP+{\angle}DEP[/tex]
[tex]90^{\circ}=35^{\circ}+{\angle}DEP[/tex]
[tex]{\angle}DEP=55^{\circ}[/tex]
Now, we know that The angle subtended at the center of a circle is double the size of the angle subtended at the edge from the same two points, therefore
[tex]{\angle}PCD=2{\angle}PED[/tex]
[tex]{\angle}PCD=2(55^{\circ})[/tex]
[tex]{\angle}PCD=110^{\circ}[/tex]
Thus, the measure of arc PD is [tex]110^{\circ}[/tex].
Hence, option (C) is correct.
