1999 AMC 8 Problems/Problem 2

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Problem

What is the degree measure of the smaller angle formed by the hands of a clock at 10 o'clock?

draw(circle((0,0),2))
dot((0,0));
for(int i = 0; i < 12; ++i)
{
dot(2*dir(30*i));
}

label("$3$",2*dir(0),W);
label("$2$",2*dir(30),WSW);
label("$1$",2*dir(60),SSW);
label("$12$",2*dir(90),S);
label("$11$",2*dir(120),SSE);
label("$10$",2*dir(150),ESE);
label("$9$",2*dir(180),E);
label("$8$",2*dir(210),ENE);
label("$7$",2*dir(240),NNE);
label("$6$",2*dir(270),N);
label("$5$",2*dir(300),NNW);
label("$4$",2*dir(330),WNW);
 (Error compiling LaTeX. dot((0,0));
^
ceab56241f8bcfa1a324787f4cf71ee92ecffb2b.asy: 6.1: syntax error
error: could not load module 'ceab56241f8bcfa1a324787f4cf71ee92ecffb2b.asy')

$\text{(A)}\ 30 \qquad \text{(B)}\ 45 \qquad \text{(C)}\ 60 \qquad \text{(D)}\ 75 \qquad \text{(E)}\ 90$

Solution

At $10:00$, the hour hand will be on the $10$ while the minute hand on the $12$.

This makes them $\frac{1}{6}$th of a circle apart, and $\frac{1}{6}\cdot360^{\circ}=\boxed{60\text{  (C)}}$.

See Also

1999 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
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
All AJHSME/AMC 8 Problems and Solutions

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