Question 1072160
<pre><font size=5><b>
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An inscribed angle is measured by one-half its intercepted arc.

Inscribed angle &#8736;CAD and &#8736;DBC both subtend the same arc CD.
So &#8736;CAD = &#8736;DBC = 30°

That means &#8736;BAD = &#8736;BAC + &#8736;CAD = 50° + 30° = 80°

Since inscribed angle &#8736;BAD is measured by one-half its
intercepted arc, its intercepted arc BCD = 2(80°) = 160°.

arc BCD + arc BAD = 360°, 

   160° + arc BAD = 360°,

          arc BAD = 200°

inscribed angle &#8736;BCD = 100° since it subtends arc BAD, and
has the measure of one-half its intercepted arc.

Edwin</pre></font></b>