A company makes 130 bags. 28 of the bags have buttons but no zips.
33 of the bags have zips but no buttons.
49 of the bags have neither zips nor buttons.
How many bags have zips on them?

Arandom high school question but a hard one

True or false? a triangle can be circumscribed about a given circle

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.