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The consecutive angles of a particular trapezoid form an arithmetic sequence. If the largest angle measures 140 degrees , what is the measure of the smallest angle?

 Nov 27, 2022
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 The sum of all interior angles of a trapezoid==360 degrees

 

260 - 140 ==220 - sum of the remaining 3 angles.

 

a+b+c+140 ==360,   

140 - c==c  -  b,   

c  -  b==b  -  a, solve for a, b, c

 

a ==40 degrees

b ==220 / 3 ==73 + 1/3 degrees

c ==320 / 3 ==106  + 2/3 degrees.

 

So, the 4 angles are: 40,  73 1/3,  106 2/3,  140

 

And the smallest angle ==40 degrees.

 Nov 27, 2022

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