Question

question 3 of 10
what is the measure of \\(\angle abc\\)?
a. \\(126^\circ\\)
b. \\(63^\circ\\)
c. \\(82^\circ\\)
d. \\(44^\circ\\)

Explanation:

Step1: Find arc AE measure

The total circle is $360^\circ$. Subtract given arcs:
$360^\circ - 82^\circ - 44^\circ = 234^\circ$

Step2: Find arc CAE measure

Add arc CA and arc AE:
$82^\circ + 234^\circ = 316^\circ$

Step3: Calculate inscribed angle ∠ABC

Use inscribed angle formula: $\frac{1}{2} \times$ (arc CAE - arc CE)
First find arc CE: $44^\circ + 180^\circ - 234^\circ = -10^\circ$ (correction: arc CE is the arc opposite ∠ABC, so use the intercepted arcs: $\angle ABC = \frac{1}{2} \times (\text{arc } AC + \text{arc } DE)$
Wait, correct approach: ∠ABC is an inscribed angle intercepting arcs AC and DE.
$\angle ABC = \frac{1}{2} \times (82^\circ + 44^\circ)$
$\angle ABC = \frac{1}{2} \times 126^\circ = 63^\circ$

Answer:

B. $63^\circ$