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Trapezium Arch

Stage: 3 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

 
 
 

Arch with an extra stoneConsider the ten trapezia. Add an eleventh trapezium to one edge of the arch.
To move from the left of the arch to the right, each trapezium has to turn the same number of degrees.

Consider the blue edgeof the bottom left hand stone. To complete the arch it has to turn a total of $180$ degrees in 10 steps. That is $18$ degrees for each step, or $9$ degrees for each of the base angles of each trapezium.


Therefore the largest angles of each trapezium are $(90+9)$ degrees and the smallest $(90-9)$ degrees = 81 degrees .
 

This problem is taken from the UKMT Mathematical Challenges.
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