Theorems, Formula Circles Quiz

In the accompanying pentgon ABCDE is inscribed in circle o, chords EC and DB intersect at F, chord DB is entended to G and tangent GA is drawn

Find
• mBDE
• mBFC
• mAGD

Answer

To solve this probelm, you must remember how to find the meaure of the interior angles of a regular polygon. In the case of a pentagon, the interior angles have a measure of (5-2) •180/5 = 108 °. Therefore, each inscribed angle creates an arc of 216°. Use the inscribed angle formula and the formula for the angle of a tangent and a secant to arrive at the angles

mBDE = 72 °

mBFC = 72 °

mAGD = ½(144 −72) = 36 °