Question

Rectangle AGNF is inscribed in the circle below. If arc AF measures 80 degrees, which is the difference between the measures of arcs AG and GN?


Answer 20 degrees
25 degrees
30 degrees
40 degrees

Answer 1

Since AGNF is a rectangle, then arcs AF and GN must be equal, and arcs AG and FN are equal. That means that arc GN equals 80.
Now, since you know that all the arcs must add up to 360, and you already have 160 degrees covered (by arcs AF and GN), we can say that...
360-160 = arc AG + arc FN
200 = arc AG + arc FN

and since AG and FN are equal, both of them equal 100 degrees.

So arc AG - arc GN =
100 - 80 = 20
the answer is 20 degrees

Answer 2

thank you

Answer 3

Glad to help and your welcome.