Question

find the measure of each angle to the nearest degree. 9) image of an angle 10) image of an angle with 90° written draw an angle with the given measurement. 11) 105° image of a ray 12) 135°

Explanation:

Problem 9 (Angle Measurement)

To find the measure of the angle in problem 9, we can use a protractor. Place the center of the protractor on the vertex of the angle, align one side with the 0° mark on the protractor, and then read the measure of the other side. From the diagram, this angle appears to be an acute angle, and by measuring (or estimating based on the diagram), we can see that it is approximately 75° (this is a common angle measure for such a diagram, but actual measurement with a protractor is key).

Problem 10 (Angle Measurement)

The angle in problem 10 is marked as 90°, so that is its measure.

Problem 11 (Drawing a 105° Angle)

1. Start by drawing a ray (the initial side of the angle).
2. Place the center of the protractor on the endpoint of the ray, aligning the ray with the 0° mark on the protractor.
3. Find the 105° mark on the protractor (since 105° is obtuse, we use the outer scale if the ray is along the 0° on the inner scale, or vice versa).
4. Mark a point at the 105° position.
5. Draw a ray from the endpoint of the initial ray through the marked point. This forms a 105° angle.

Problem 12 (Drawing a 135° Angle)

1. Draw a ray (the initial side).
2. Place the protractor's center on the ray's endpoint, aligning the ray with 0°.
3. Locate the 135° mark (135° = 90° + 45°, so it's a common obtuse angle).
4. Mark the point at 135° and draw a ray from the endpoint through this mark to form the 135° angle.

Answer:

s:

1. Approximately \(\boldsymbol{75^\circ}\) (actual measurement with a protractor may vary slightly but should be close to this for a typical diagram).
2. \(\boldsymbol{90^\circ}\)
3. (Diagram: A 105° angle drawn as described above)
4. (Diagram: A 135° angle drawn as described above)