Question

if $\angle abc$ measures $65^\circ$, what is the measure of $\overarc{adc}$?
a. $130^\circ$
b. $295^\circ$
c. $65^\circ$
d. $230^\circ$

Explanation:

Step1: Recall full circle measure

A full circle has a measure of $360^\circ$.

Step2: Identify arc matching central angle

The central angle $\angle ABC = 65^\circ$, so the arc $\widehat{AC}$ it intercepts also measures $65^\circ$.

Step3: Calculate $\widehat{ADC}$

Subtract $\widehat{AC}$ from the full circle:
$\widehat{ADC} = 360^\circ - 65^\circ$

Answer:

D. $230^\circ$