You may also like

problem icon

14 Divisors

What is the smallest number with exactly 14 divisors?

problem icon

Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

problem icon

Dozens

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Weekly Problem 44 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1



The exterior angles of a regular nonagon are $360^{\circ}\div 9 = 40^{\circ}$, whence the interior angles are $180^{\circ} - 40^{\circ}= 140 ^{\circ}$.
 
In the arrowhead quadrilateral whose rightmost vertex is X, three of the angles are $40^{\circ}$, $40^{\circ}$ and $360^{\circ} - 140^{\circ}=220^{\circ}$ and these add up to $300^{\circ}$.
 
So the agle at X is $60^{\circ}$.
 
[It is now posible to see that the entire nonagon can fit neatly inside an equilateral triangle and so the angle X $60^{\circ}$ ]
 
 

This problem is taken from the UKMT Mathematical Challenges.

View the previous week's solution
View the current weekly problem