kitchen table math, the sequel: help desk - how many vertical angles

Thursday, April 7, 2011

help desk - how many vertical angles

Here's a problem from The Art of Problem Solving Counting Introduction to Counting and Probability by David Patrick:
How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?

p. 64

3 comments:

Daniel Ethier said...

A pair of vertical angles is formed by two lines.

You have five lines to choose those two lines from. You have five ways to choose the first line and four ways to choose the second line. But order doesn't matter, so 10 pairs.

gasstationwithoutpumps said...

Almost, Daniel. You forgot, though that a pair of lines forms TWO pairs of vertical angles.

Catherine Johnson said...

oh!

That's my problem --- I got Daniel's answer --- wasn't thinking about the fact that a pair of vertical lines forms TWO PAIRS of angles!

Thank you!