We use a protractor to measure angles. A protractor is an instrument that looks as follows:
To find the measure of an angle using a protractor, we follow three steps:
Place the midpoint of the protractor on the vertex of the angle.
Align one side of the angle with the line passing through the midpoint and zero on the protractor.
Read off the degrees where the other side of the angle intersects the scale.
Let's measure the following angle using a protractor.
We place the midpoint of our protractor on the vertex and align a zero on the protractor with one of the sides.
Reading the protractor, we see that the angle measures
Warning: Protractors usually have two scales in opposite directions. Be careful which one you use. In this case, we used the upper scale because this is the one that starts from zero as we measure counterclockwise.
Determine the measure of the angles shown below.
We will use a protractor to determine the measure of the angles.
To do this, we align one side of an angle with the zero mark (on the left or on the right side of the protractor) and read the degrees where the second side of the angle intersects the scale of numbers:
By doing this, we get the following angle measures.
Determine the measure of the angle $\angle ABC$ shown above.
|
a
|
$24^\circ$ |
|
b
|
$162^\circ$ |
|
c
|
$22^\circ$ |
|
d
|
$158^\circ$ |
|
e
|
$145^\circ$ |
Determine the measure of the angle $\angle ABC$ shown above.
|
a
|
$105^\circ$ |
|
b
|
$120^\circ$ |
|
c
|
$130^\circ$ |
|
d
|
$114^\circ$ |
|
e
|
$118^\circ$ |
Determine the measure of the angle shown below.
To find the angle, we can use either scale of the protractor.
First, let's use the upper scale. The side of the angle intersects the upper scale at and the other side intersects the upper scale at To find the measure of we subtract the smaller reading from the larger one and get
If we use the lower scale, we get the same result. The side of the angle intersects the lower scale at and the other side intersects the lower scale at Subtracting the smaller reading from the larger one, we get
We can check our result by rotating the protractor to align its zero with the side as shown below. This way, we can perform the usual process, taking only a single measurement. Indeed, we see that is equal to
Determine the measure of the angle $\angle ABC$ shown above.
|
a
|
$80^\circ$ |
|
b
|
$65^\circ$ |
|
c
|
$40^\circ$ |
|
d
|
$115^\circ$ |
|
e
|
$85^\circ$ |
Determine the measure of the angle $\angle ABC$ shown above.
|
a
|
$110^\circ$ |
|
b
|
$100^\circ$ |
|
c
|
$95^\circ$ |
|
d
|
$105^\circ$ |
|
e
|
$115^\circ$ |