Question

Find the measure of arc ABC.

Answer 1

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):

`65=(1)/(2)(x-[360-x])` 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.