Question

In the circle below, segment AB is tangent to circle C and segment DE is parallel to segment AB.
If arc DE is 78 degrees, what is the measure of arc AD?

Answer 282 degrees
141 degrees
360 degrees
78 degrees

Answer 1

If AB is tangent to the circle, it only intersects it at one point. Then is DE is parallel to AB, the distance from this intersection (A) to D and the distance to E must be the same. Since a circle has a full measure of 360 degrees,\
AD + DE + EA = 360
AD + AE = 360 - 78 = 282
But AD = AE, so 2*AD = 282
AD = 141

Answer 2

thank you so much