use the protractor to measure the angle. ∠ def = \\boxed{} ^\\circ

Answer

Explanation:

Step1: Identify the angle's sides

The angle ∠DEF has vertex at E, with one side along the base (from E to the right, near 0°) and the other side (ED) at a certain mark on the protractor.

Step2: Read the protractor scale

The side EF is near the 20° mark (wait, no, let's check again). Wait, the base is along the 0° - 180° line. The ray ED is at 150°? Wait, no, the protractor: the left side (ED) is at 150°? Wait, no, the protractor has 0° on the right, 180° on the left. Wait, the ray EF is at 20°? Wait, no, let's look at the positions. Wait, the angle between ED and EF: the protractor's center is at E. The ray EF is at 20° (since from 0°, moving up to F, which is at 20°? Wait, no, the marks: the right side is 0°, then 10°, 20°, etc. Wait, no, the protractor in the image: the right side is 0°, and the left is 180°. The ray ED is at 150° (since from 180°, moving towards D, which is at 150°? Wait, no, let's calculate the angle between the two rays. The ray along the base (right) is at 0°, and the ray ED is at 150°? Wait, no, the angle between them is 150° - 20°? Wait, no, wait: the ray EF is at 20° (from 0°), and the ray ED is at 150° (from 0°)? Wait, no, the protractor: the numbers on the top arc: 0° at right, 180° at left. Wait, the angle ∠DEF: the two sides are ED and EF, with E as the vertex. The side EF is at 20° (from 0°), and the side ED is at 150° (from 0°)? Wait, no, the angle between them is 150° - 20°? No, wait, the straight line is 180°, but the angle here is between ED and EF. Wait, looking at the protractor: the ray EF is at 20° (since the mark at F is at 20°), and the ray ED is at 150° (since the mark at D is at 150°). Wait, no, the angle between them is 150° - 20°? No, that can't be. Wait, no, the protractor: the center is E. The ray along the base (right) is 0°, and the ray ED is at 150° (because from 0°, moving counterclockwise to ED, which is at 150°). Wait, no, the angle between EF (at 20°) and ED (at 150°) is 150° - 20° = 130°? Wait, no, wait, maybe I got the scales wrong. Wait, the protractor has two scales: the inner and outer? No, in this image, the top scale: 0° at right, 180° at left. So the angle between the two rays: one is at 20° (EF) and the other at 150° (ED). So the angle is 150° - 20° = 130°? Wait, no, wait, let's check again. Wait, the ray EF is at 20° (from 0°), and the ray ED is at 150° (from 0°). So the angle between them is 150 - 20 = 130 degrees. Wait, but let's confirm: the straight line is 180°, but the angle here is between ED and EF. So if EF is at 20° (from 0°) and ED is at 150° (from 0°), then the angle is 150 - 20 = 130°. Wait, but maybe I made a mistake. Wait, the protractor: the mark at F is at 20° (since from 0°, the next mark is 10°, then 20°), and the mark at D is at 150° (from 0°). So the angle between them is 150 - 20 = 130 degrees.

Step3: Calculate the angle

The angle ∠DEF is the difference between the two positions on the protractor. The ray EF is at 20° (from 0°), and the ray ED is at 150° (from 0°). So 150 - 20 = 130 degrees.

Answer:

130