Counting

How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?

Vicky.

Thanks.

Hello, Vicky!

Quote:

How many pairs of vertical angles are formed by five distinct lines
that have a common point of intersection?

Code:

* * J * A * * * * * * * I * * * B * * * * * * * * * * * * * * * * *** * H * C * *** * * * * * * * * * * * * * * * * G * * * D * * * * * * * F * E * *

I found twenty pairs.

In the list below, $A$ means $\angle A$
. . and $AB$ means $A+B.$

. . . . . . . . . . . . $(A|F),\;(B|G),\;(C|H),\;(D|I),\;(E|J)$

. . . . . . . . $(AB|FG),\;(BC|GH),\;(CD|HI),\;(DE|IJ),\;(EF|JA)$

. . . . $(ABC|FGH),\;(BCD|GHI),\;(CDE|HIJ),\;(D{E}F|IJA),\; (EFG|JAB)$

$(ABCD|FGHI),\;(BCDE|GHIJ),\;(CD{E}F|HIJA),\;(D{E}F G|IJAB),$ $\;(EFGH|JABC)$

Thank You!!!!!!!!!!!!!!!!!!!!(Rofl)

Vicky.