Question

m\\(\widehat{ab}\\)= ?
m\\(\angle aeb\\)= ?
m\\(\angle acb\\)= ?
m\\(\widehat{adb}\\)= ?
20°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. $\angle ADB = 20^{\circ}$, so $m\overset{\frown}{AB}=2\times20^{\circ}=40^{\circ}$.

Step2: Central - angle and arc relationship

The central angle $\angle AEB$ has the same measure as the arc it subtends. So $m\angle AEB = 40^{\circ}$.

Step3: Inscribed - angle on the same arc

$\angle ACB$ and $\angle ADB$ are inscribed angles on the same arc $\overset{\frown}{AB}$, so $m\angle ACB = 20^{\circ}$.

Step4: Semicircle and arc measure

The whole circle is $360^{\circ}$, so $m\overset{\frown}{ADB}=360^{\circ}-40^{\circ}=320^{\circ}$.

Answer:

$m\overset{\frown}{AB}=40^{\circ}$
$m\angle AEB = 40^{\circ}$
$m\angle ACB = 20^{\circ}$
$m\overset{\frown}{ADB}=320^{\circ}$