Question

Segments AC and BD are diameters of Circle E. If, arc ACD = 326 degrees then what does BCA equal?

Answer 1

Since arc ACD is 326 degrees and arc AD is a semicircle (180 degrees), then arc ACB is:

arc ACB = arc ACD - arc AD

arc ACB = 326 - 180

arc ACB = 146 degrees

Since arc ACB is a central angle, it is equal to twice the inscribed angle BCA:

2 * BCA = arc ACB

BCA = arc ACB / 2

BCA = 146 / 2

BCA = 73 degrees

Therefore, BCA is 73 degrees.