Secants, Tangents, and Angles Answers

Circle Z is shown. Chords A C and B D intersect. The measure of arc C D is 147 degrees and the measure of arc A B is 133 degrees. Angle 2 intercepts the arc with measure 147 degrees. Angle 1 intercepts the arc with measure 133 degrees.

Circle O is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is d, and the second arc formed is b. Arcs a and c are the other 2 arcs outside of the secants.

Circle P is shown. Tangents X Y and Z Y intersect at point Y outside of the circle to form an angle with measure 72 degrees. The first arc formed has a measure of x degrees, and the second arc has a measure of (360 minus x) degrees.

A secant and a tangent meet at a 90° angle outside the circle. What must be the difference between the measures of the intercepted arcs?

Circle Q is shown. Secant L N and tangent P N intersect at point N outside of the circle. Secant L N intersects the circle at point M. Arc M P is y, arc L P is x, and arc M L is z.

Circle O is shown. Tangents C B and A B intersect at point B outside of the circle. The measure of the first arc formed is 150 degrees, and the measure of the second arc formed is 210 degrees.

Circle C is shown. 2 secants intersect at a point outside of the circle to form angle 1. The first arc formed is 36 degrees, and the second arc formed is 106 degrees.