Draw the lines through the vertices
of angles 2,3,4,5, parallel to the lines marked with arrowheads. If two lines
are parallel, alternate angles are equal. So,
(1)angle 1 is equal to upper half of angle
2
(2)lower half of angle 2 is equal to upper
half of angle 3
(3)lower half of angle 3 is equal to upper
half of angle 4
(4)lower half of angle 4 is equal to upper
half of angle 5
(5)lower half of angle 5 is equal to angle 6.
Therefore, the sum of the odd numbered
angles and the sum of the even numbered angles are always equal.
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Hi, Richard.
I think the answer is like this.
Draw the lines through the vertices of angles 2,3,4,5, parallel to the lines marked with arrowheads. If two lines are parallel, alternate angles are equal. So,
(1)angle 1 is equal to upper half of angle 2
(2)lower half of angle 2 is equal to upper half of angle 3
(3)lower half of angle 3 is equal to upper half of angle 4
(4)lower half of angle 4 is equal to upper half of angle 5
(5)lower half of angle 5 is equal to angle 6.
Therefore, the sum of the odd numbered angles and the sum of the even numbered angles are always equal.
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Yes very good, that's right! Rather a neat little problem I thought