- Angles can be measured using a protractor and estimated using common referent angles like 45, 90, and 180 degrees. - True bearing is the angle measured clockwise from true north to a destination, with north defined as 0 degrees. - Examples show how to determine true bearing by drawing a line north from the starting point and measuring the clockwise angle to the destination using a protractor.

1. Measuring, Drawing and Estimating Angles
Slide 1
Definitions:
Angle: two rays that meet at a point called the vertex.
Angle Measure: a number representing the spread of the two rays
of an angle, expressed in degrees.
Angle Referent: a common standard of angle measure, for
example, 90, 45, 30 and 22.5 used to estimate angles.
True Bearing: the angle measured clockwise between true north
and an intended path or direction, expressed in degrees.

2. Slide 2
In many jobs, people have to draw angles or estimate their measure.
To estimate the size of an angle, you can use referent angles, which
are angles that are easy to visualize.
Using a protractor, measure the following angles. Write your measures
on a piece of paper. Advance to the next slide to check your answers.
Referent Angles

3. Slide 3
In many jobs, people have to draw angles or estimate their measure.
To estimate the size of an angle, you can use referent angles, which
are angles that are easy to visualize.
Using a protractor, measure the following angles… enter your answer
in the text box provided. Click on “Check” to check your answer.
Referent Angles
90° 45° 30° 60°

4. Slide 4
The following referents are the most commonly used.
Referent Angles
Use the referents above to estimate the size of each of the following angles.

5. C is close to a
straight angle so it is
probably around 170°
B is more than 60°
referent but less
than 90° referent so
it is probably
around 80°
A is slightly
bigger than the 45°
referent so it’s
probably around 50°
Slide 5
The following referents are the most commonly used.
Referent Angles
Use the referents above to estimate the size of each of the following angles.

6. Slide 6
In navigation and map-making, people often
measure angles from the vertical, or north.
The angle, measured in a clockwise direction
from a line pointing north, is referred to as
the true bearing.
Working with True Bearing
Straight north has a bearing of 0°.

7. Slide 7
Advance to the next slide to see the true bearings
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

8. Slide 8
Advance to the next slide to see the true bearings
N – true bearing 0°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

9. Slide 9
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

10. Slide 10
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
E – true bearing 90°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

11. Slide 11
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
E – true bearing 90°
SE – true bearing 135°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

12. Slide 12
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
E – true bearing 90°
SE – true bearing 135°
S – true bearing 180°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

13. Slide 13
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
E – true bearing 90°
SE – true bearing 135°
S – true bearing 180°
SW – true bearing 225°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

14. Slide 14
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
E – true bearing 90°
SE – true bearing 135°
S – true bearing 180°
SW – true bearing 225°
W – true bearing 270°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

15. Slide 15
Advance to the next slide to see the true bearings
N – true bearing 0°
NE – true bearing 45°
E – true bearing 90°
SE – true bearing 135°
S – true bearing 180°
SW – true bearing 225°
W – true bearing 270°
NW – true bearing 315°
NOTE: This slide will not advance to the
following slide. To go to the next slide,
you must click the forward button.

16. Slide 16
Example 1:
Determine the true bearing between A and B.

17. Step 1 – draw a line from point A
straight North
Slide 17
Example 1:
Determine the true bearing between A and B.

18. Step 1 – draw a line from point A
straight North
Slide 18
Example 1:
Determine the true bearing between A and B.
Step 2 – align protractor with 0
along the line pointing North

19. Step 1 – draw a line from point A
straight North
Slide 19
Example 1:
Determine the true bearing between A and B.
Step 2 – align protractor with 0
along the line pointing North
Answer:
The true bearing between points A and B is 70.
Step 3 – measure the angle

20. Slide 20
Example 2:
Determine the true bearing between A and B.

21. Step 1 – draw a line from point A
straight North
Slide 21
Example 2:
Determine the true bearing between A and B.

22. Step 1 – draw a line from point A
straight North
Slide 22
Example 2:
Determine the true bearing between A and B.
Step 2 – align protractor with 0
along the line pointing North

23. Step 1 – draw a line from point A
straight North
Slide 23
Example 2:
Determine the true bearing between A and B.
Step 2 – align protractor with 0
along the line pointing North
Step 3 – mark off the angle of
180 from N.

24. Step 1 – draw a line from point A
straight North
Slide 24
Example 2:
Determine the true bearing between A and B.
Step 2 – align protractor with 0
along the line pointing North
Step 3 – mark off the angle of
180 from N.
Step 4 – measure the angle
starting from the mark (step 3)
and add 180
68 + 180 = 248
Answer:
The true bearing between points A and B is 248.