Question

what is the measure of \\( \angle rcp \\) in the figure below?
a. \\( 35 ^ { \circ } \\)
b. \\( 55 ^ { \circ } \\)
c. \\( 11 ^ { \circ } \\)
d. \\( 60 ^ { \circ } \\)
e. \\( 70 ^ { \circ } \\)
f. cannot be determined

Explanation:

Step1: Recall the Angle Bisector Theorem

If a point is equidistant from the sides of an angle, then it lies on the bisector of the angle. Here, \(DP = DR=11\), so \(CD\) is the angle bisector of \(\angle RCP\).

Step2: Calculate \(\angle RCP\)

Since \(CD\) is the angle bisector of \(\angle RCP\), \(\angle RCP = 2\times\angle DCP\). Given \(\angle DCP = 35^{\circ}\), then \(\angle RCP=2\times35^{\circ}\)

Answer:

\(70^{\circ}\), so the answer is E.