Question

find the measure of each angle to the nearest degree.

1. image of an angle
2. image of a right angle labeled 90°

draw an angle with the given measurement.

1. 105° image of a ray
2. 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, the angle appears to be an acute angle, and by measuring (or comparing with known angles), we can estimate it. Let's assume we use a protractor:

Step 1: Align Protractor

Place the protractor's center on the angle's vertex, align one ray with the 0° line.

Step 2: Read the Measure

Read the degree where the other ray intersects the protractor. Let's say the measurement is approximately 75° (this can vary slightly based on the diagram's drawing, but a typical acute angle like this is around 75° - 80°, let's take 75° for example).

Problem 10 (Angle Measurement)

The angle is marked as 90°, so we can confirm it's a right angle. So the measure is 90°.

Problem 11 (Drawing 105° Angle)

Step 1: Draw a Ray

Start by drawing a ray (one side of the angle) with a straightedge.

Step 2: Use Protractor

Place the center of the protractor on the endpoint of the ray (the vertex), align the ray with the 0° mark on the protractor.

Step 3: Mark 105°

Find the 105° mark on the protractor and make a small dot at that position.

Step 4: Draw the Second Ray

Use a straightedge to draw a ray from the vertex through the dot. This forms a 105° angle.

Problem 12 (Drawing 135° Angle)

Step 1: Draw a Ray

Draw a ray (initial side) with a straightedge.

Step 2: Use Protractor

Place the protractor's center on the ray's endpoint, align the ray with the 0° mark.

Step 3: Mark 135°

Locate the 135° mark on the protractor and mark a point.

Step 4: Draw the Second Ray

Draw a ray from the vertex through the marked point to form the 135° angle. Alternatively, since 135° = 90° + 45°, you can draw a right angle (90°) and then add a 45° angle to it.

Answer:

s:

1. Approximately \(\boldsymbol{75^\circ}\) (or other reasonable acute angle measure based on diagram)
2. \(\boldsymbol{90^\circ}\)
3. (Angle drawn with measure \(105^\circ\))
4. (Angle drawn with measure \(135^\circ\))

(Note: For problems 11 and 12, the answer is the drawn angle, and the steps above guide the drawing process. For problem 9, the measure is an estimate based on the diagram's appearance, and problem 10 is given as \(90^\circ\).)