The figure below shows a triangle with vertices a and b on a circle and vertex c outside it. side ac is tangent to the circle. side bc is a secant intersecting the circle at point x: the figure shows a circle with points a and b on it and point c outside it. side bc of triangle abc intersects the circle at point x. a tangent to the circle at point a is drawn from point c. arc ab measures 152 degrees and angle cba measures 64 degrees. what is the measure of angle acb? 32° 6° 24° 12°

12° is the measure of ∠acb

step-by-step explanation:

the figure shows a circle with points a and b on it and point c outside it. side bc of triangle abc intersects the circle at point x

a tangent to the circle at point a is drawn from point c

see the attachment for figure.

arc ab measures 152° and ∠cba measures 64°

the angle subtended at any point on the circumference is half the angle subtended by an arc at the center of a circle.

alternate segment theorem: the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment.

exterior angle theorem: it states that sum of two opposite angles of triangle is equal to exterior angle.

thus, 12° is the measure of ∠acb

the answer is 8/21

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