1. ## Counting

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

Vicky.

Thanks.

2. 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 $\displaystyle A+B.$

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

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

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

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

3. Thank You!!!!!!!!!!!!!!!!!!!!

Vicky.