Question

question 25 of 44
what is the measure of ( angle doc ), given that ( overarc{ab} cong overarc{dc} )?
diagram of a circle with center ( o ), points ( a, b, c, d ); ( angle aob = 65^circ )
a. ( 65^circ )
b. ( 115^circ )
c. ( 295^circ )
d. ( 25^circ )

Explanation:

Step1: Recall the property of congruent arcs

In a circle, congruent arcs correspond to congruent central angles. Given that \(\widehat{AB} \cong \widehat{DC}\), their central angles \(\angle AOB\) and \(\angle DOC\) are equal.

Step2: Identify the measure of \(\angle AOB\)

From the diagram, \(\angle AOB = 65^\circ\). Since \(\angle DOC\) is equal to \(\angle AOB\) (because \(\widehat{AB} \cong \widehat{DC}\)), we have \(\angle DOC = 65^\circ\).

Answer:

A. \(65^\circ\)