Difference between revisions of "1990 AHSME Problems/Problem 3"
(Created page with "== Problem == The consecutive angles of a trapezoid form an arithmetic sequence. If the smallest angle is <math>75^\circ</math>, then the largest angle is <math>\text{(A) } 95^...") |
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== Solution == | == Solution == | ||
| − | <math>\fbox{ | + | A trapezoid is a quadrilateral; therefore the interior angles sum to <math>360^\circ</math>. |
| + | Thus <math>75+(75+x)+(75+2x)+(75+3x)=360</math>, so <math>x=10</math> and the largest angle is <math>105^\circ</math> which is <math>\fbox{C}</math> | ||
== See also == | == See also == | ||
Latest revision as of 02:44, 4 February 2016
Problem
The consecutive angles of a trapezoid form an arithmetic sequence. If the smallest angle is 
, then the largest angle is
Solution
A trapezoid is a quadrilateral; therefore the interior angles sum to 
.
Thus 
, so 
and the largest angle is 
which is 
See also
| 1990 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
