Question 1194108
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Two tangents to a circle from the same point are congruent.  So triangle ABC is isosceles with base angles BCA and CBA and vertex angle  A.<br>
(1) Use that and the fact that the sum of the angles in a triangle is 180 degrees to find the measures of angle A and angle ABC.<br>
(2) The two tangents cut the 360 degrees of the circle into two parts.  If arc BC is x degrees, then the other arc is 360-x degrees.<br>
Then the measure of angle A is half the difference between the measures of the two arcs:<br>
{{{A = (1/2)((360-x)-x)}}}<br>
Use that and the measure of angle A that you found in part (1) to find x, which is the degree measure of arc BC.<br>
(3) It is impossible to find the measure of angle BDC, since point D is nowhere defined.<br>