questions in attachments.
13.
$\displaystyle m\widehat{AB}=52^{\circ} \ \ $ because an inscribed angle is equal to half its intercepted arc.
$\displaystyle m\angle D=26^{\circ} \ \ $ because inscribed angles that intercept the same arc are equal in measure.
14.
$\displaystyle m\angle B=90^{\circ} \ \ $ because an inscribed angle in a semicircle always measures 90 degrees. It subtends 180 degrees and is equal to half of it. You don't have 90 degrees as a choice. Somebody messed up.
$\displaystyle m\widehat{AD}=180-70=110^{\circ} \ \ $ because arcs CD and AD make up a semicircle (180 degrees).