Hello, Vicky!
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, $\displaystyle A$ means $\displaystyle \angle A$
. . and $\displaystyle AB$ means $\displaystyle A+B.$
. . . . . . . . . . . . $\displaystyle (A|F),\;(B|G),\;(C|H),\;(D|I),\;(E|J) $
. . . . . . . . $\displaystyle (AB|FG),\;(BC|GH),\;(CD|HI),\;(DE|IJ),\;(EF|JA)$
. . . . $\displaystyle (ABC|FGH),\;(BCD|GHI),\;(CDE|HIJ),\;(D{E}F|IJA),\; (EFG|JAB)$
$\displaystyle (ABCD|FGHI),\;(BCDE|GHIJ),\;(CD{E}F|HIJA),\;(D{E}F G|IJAB),$ $\displaystyle \;(EFGH|JABC)$