# Counting

• Aug 10th 2009, 03:59 PM
Vicky1997
Counting
How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?

Vicky.

Thanks.
• Aug 10th 2009, 06:15 PM
Soroban
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 $A+B.$

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

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

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

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

• Aug 10th 2009, 06:32 PM
Vicky1997
Thank You!!!!!!!!!!!!!!!!!!!!(Rofl)

Vicky.