Finding the Measure of Clock Angles

Finding the Measure of Clock Angles 1.2 Measurement of Segments and Angles

There are many ways to find the measure of the angle formed by the hands of an analog clock. • You may use one of the methods shown or find your own method (that can be justified logically and mathematically) Methods

Determine the rate of the hour hand. • Determine the rate of the minute hand. Algebraic Method #1

Convert the total time to minutes and multiply by the hour rate. • Multiply the number of minutes by the minute rate. • Find the measure of the clock angles by taking the difference. Make sure this is the minor angle formed. Algebraic Method #1

Long (minute) hand = 6°⁄min. Multiply #minutes by 6. • Short (hour) hand = #hours x 30° + “long”/12 because long had travels 12 times faster. • Measure of clock angle equals the difference. Remember to subtract from 360°, if not a minor angle. Algebraic Method #2

Each interval between numbers is 30°. • Determine the number of “whole” intervals between the hands. • Calculate the number of degrees for any fractional parts of intervals. The diagrams that follow illustrate this process. Fractional Intervals

4:38 = 89° 18º 11º 60°

4:38 = 89° 19º 18º 90°

11:14 = 107° 7º 23º 24º 60°

10:24 = 168° 12º 150º 6°

7:42 = 21° 30º 21º 9º 12°

1:53 = 98.5° 12º 26.5º 60°

12:33 =181.5° 360 – 181.5 = 178.5° 13.5º 16.5º 150º 18º 12º 150°

12:20

Finding the Measure of Clock Angles