Answer:
Step-by-step explanation:
The angle (angle D) created by 2 tangents to a circle (DC and DA) is half of the difference between its intercepted arcs (arc ABC - arc AC):
[tex]65=\frac{1}{2}(x-[360-x])[/tex] If we don't know the measures of either of the arcs, but we DO know that the measure around the outside of a circle is 360 degrees, then we will call arc ABC "x", making arc AC "360 - x". Solving:
2(65) = 2x - 360 and
130 = 2x - 360 and
130 + 360 = 2x and
490 = 2x so
x = 245. This means that arc ABC is 245 and arc AC is 115.
