Prove that given any 17 integers, there exist nine of them whose sum is divisible by 9.

(it might to use the fact that given any five integer you can find three whose sum is divisible by 3)

This is a simple consequence of the Zero-sum problem: https://en.wikipedia.org/wiki/Zero-sum_problem

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh