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Angles, from basic rules to circle theorems

Angles on Lines and Points

You may also like. English Quiz. Synonyms of. French Translation of. Word List. Word of the day:. Hindi Translation of. NEW from. Collins English Dictionary. Word origin. Angle in British English Word Frequency. Angle in American English Word Frequency. All rights reserved. Informal a. Informal to give a specific point of view to a story , report , etc. Example sentences including angle. These examples have been automatically selected and may contain sensitive content.

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Measure and classify an angle

Week 6. About this free course 24 hours study.

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Free statement of participation on completion of these courses. Badge icon Earn a free Open University digital badge if you complete this course, to display and share your achievement. Course content Course content. Figure 1 Angles in different anticlockwise turns. Long description. Figure 2 Parallel lines. Previous 1 Geometry. Next 1. To do this, align the sighting marks of the compass with this point. At the intersection of the sighting line and the graduated ring, read the azimuth of the line from the point of observation. The reading will be most accurate if you limit the length of the sighting line to 40 to m.

Place more ranging poles on the line as you need them. Note: to check the value of an azimuth, turn around and look in the opposite direction at another point on the same line. If the difference is small enough, you can ignore it, or correct it by averaging the two readings. If it is large, you have made an error which you should correct. This is the forward azimuth. To measure a horizontal angle, stand at the angle's summit and measure the azimuth of each of its sides; calculate the value of the angle as follows. If the magnetic north falls outside the angle, calculate the value of the angle between the two lines of sight as equal to the difference between their azimuths.

Always subtract the smaller number from the larger one, no matter which azimuth you read first. Just be sure that the magnetic north is not inside the angle. YA - Az. AF- Az. AE Note: to check on your measurements and to improve their accuracy, you should repeat each measurement three times from the same station.


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These measurements should give similar results. If you cannot reach the summit of the angle, separately measure the azimuth of each line from another point situated on it see step 8, above and calculate the angle as in step 9, above. For each side of the polygon , you will thus determine one forward and one rear azimuth.

To do this, add the two numbers and divide by two. From averages like this for the other pairs of azimuths, you can calculate the interior angles of the polygon , as explained above. Note : to make a final check, add all the interior angles. Proceed in the same way from the other three summits C, D and E. In total, you get ten measurements.

Mark them down in your notebook.

Angles – Mathematics GCSE Revision – Revision Maths

See columns 1 and 2 where the order of measurements is shown in parentheses. This gives you values which should be equal to the smallest observed azimuths, written either in column 1 or in column 2, according to the position of the summit. When the values are equal to the smaller observed azimuths summits C,E , transfer these measurements to columns 4 or 5, according to the type of azimuth they represent. When they are not equal summits A, B, D : Use columns 1 or 2 and column 3 to calculate the average smallest azimuth.

To do this, add the measurement of the smallest Az from column 1 or 2 to the number in column 3. Divide the total by 2 to find the average. Enter a forward Az in column 4 and a rear Az in column 5. As before, enter a forward Az in column 4 and a rear Az in column 5. If you have to measure consecutive angles , proceed as described earlier see end of Section 3.

When using a magnetic compass to measure horizontal angles, you should carefully check the following points:. The magnetic needle must swing freely on its pivot. Keep the compass horizontal in one hand and, with the other hand, bring an iron object close to the magnetized needle's point. Make the needle move to the left with the iron; when you move the iron away, the needle should swing quickly and smoothly to its original position. Repeat the movement in the opposite direction to double check.