SOLUTION: ABCD is a cyclic quadrilateral whose diagonals intersect at P such that angle DBC=30 degree and angle BAC=50 degree. Find angle BCD and angle CAD.

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Question 1072160: ABCD is a cyclic quadrilateral whose diagonals intersect at P such that angle DBC=30 degree and angle BAC=50 degree.
Find angle BCD and angle CAD.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!



An inscribed angle is measured by one-half its intercepted arc.

Inscribed angle ∠CAD and ∠DBC both subtend the same arc CD.
So ∠CAD = ∠DBC = 30°

That means ∠BAD = ∠BAC + ∠CAD = 50° + 30° = 80°

Since inscribed angle ∠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 ∠BCD = 100° since it subtends arc BAD, and
has the measure of one-half its intercepted arc.

Edwin