Question

The vertex of an angle measuring 32° is in the exterior of a circle and its sides are secants of the circle. If the sum of the measures of the intercepted arcs is 180°, find the measure of each intercepted arc.

Answer 1

Answer:

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Answer 2

Answer:

58° and 122°

Step-by-step explanation:

Angle A is equal to ½ of arc CE - arc BD.

Angle A is also equal to 32°

32 = ½ (CE - BD)

Arc BD + Arc CE = 180° ,  so   BD = 180° - CE

Then substitute the second equation into the first and solve

32 = ½ (CE - (180° - CE))

CE = 122°

Lastly, 180° - 122° = BD = 58°