Question

activity 3: measure me and you will see... use the figures below to answer the questions that follow. 1. what is the measure of each of the following angles in figure 1? use a protractor. a. ∠top d. ∠ros b. ∠poq e. ∠sot c. ∠qor 2. in figure 2, af, ab, ac, ad, and ae are radii of ⊙a. what is the measure of each of the following angles? use a protractor. a. ∠fab d. ∠ead b. ∠bac e. ∠eaf c. ∠cad 3. how do you describe the angles in each figure? 4. what is the sum of the measures of ∠top, ∠poq, ∠qor, ∠ros, and ∠sot in figure 1? how about the sum of the measures of ∠fab, ∠bac, ∠cad, ∠ead, and ∠eaf in figure 2?

Explanation:

Step1: Measure angles in Figure 1

Use a protractor to measure ∠TOP, ∠POQ, ∠QOR, ∠ROS, ∠SOT. The actual values will depend on the measurement with the protractor.

Step2: Measure angles in Figure 2

Use a protractor to measure ∠FAB, ∠BAC, ∠CAD, ∠EAD, ∠EAF. The actual values will depend on the measurement with the protractor.

Step3: Describe angles

In Figure 1, the angles are angles with a common vertex O. In Figure 2, the angles are central - angles of a circle with center A.

Step4: Calculate sums

For Figure 1, since the angles ∠TOP, ∠POQ, ∠QOR, ∠ROS, ∠SOT form a complete - turn around point O, the sum of their measures is 360°. For Figure 2, since ∠FAB, ∠BAC, ∠CAD, ∠EAD, ∠EAF are central angles that together make up a full - circle around point A, the sum of their measures is also 360°.

Answer:

1. The measures of the angles in Figure 1 are obtained by protractor measurement.
2. The measures of the angles in Figure 2 are obtained by protractor measurement.
3. In Figure 1, they are angles with a common vertex. In Figure 2, they are central angles of a circle.
4. The sum of the measures of ∠TOP, ∠POQ, ∠QOR, ∠ROS, and ∠SOT in Figure 1 is 360°. The sum of the measures of ∠FAB, ∠BAC, ∠CAD, ∠EAD, and ∠EAF in Figure 2 is 360°.