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.

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) (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

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