1990 AHSME Problems/Problem 3

Problem

The consecutive angles of a trapezoid form an arithmetic sequence. If the smallest angle is $75^\circ$ , then the largest angle is

$\text{(A) } 95^\circ\quad \text{(B) } 100^\circ\quad \text{(C) } 105^\circ\quad \text{(D) } 110^\circ\quad \text{(E) } 115^\circ$

Solution

A trapezoid is a quadrilateral; therefore the interior angles sum to $360^\circ$ . Thus $75+(75+x)+(75+2x)+(75+3x)=360$ , so $x=10$ and the largest angle is $105^\circ$ which is $\fbox{C}$

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
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1990 AHSME Problems/Problem 3

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