1999 AMC 8 Problem 2: Solution

Work through 1999 AMC 8 Problem 2 on angles with a written solution, hints, and a visual explanation.

GeometryLevel 1 · Warmup

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

Clock face with twelve evenly spaced hour marks; compare the positions of 10 and 12 for ten o'clock.
Diagram 1
  • A. 30
  • B. 45
  • C. 60
  • D. 75
  • E. 90
Hints
  1. See the 12 equal spaces
  2. Measure one space
  3. Count the spaces
Read the step-by-step solution

Answer: C · 60°

  1. See the 12 equal spaces

    A clock face is split into 12 equal spaces around 360 degrees.

    12 spaces around the face

  2. Measure one space

    Each hour mark is 30 degrees from the next.

    360° ÷ 12 = 30°

  3. Count the spaces

    At 10:00, the minute hand points to 12 and the hour hand points to 10. The smaller angle spans 2 hour spaces.

    2 spaces from 10 to 12

  4. Add them up

    Two 30-degree spaces make the smaller angle.

    30° + 30° = 60°

  5. Conclude

    The smaller angle is 60 degrees, so the answer is C.

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