Question

find the measure of each angle to the nearest degree.

1. image of an angle
2. image of an angle with a 90° label

draw an angle with the given measurement.

1. 105° image of a ray
2. 135°

Explanation:

Problem 9 and 10: Find the measure of each angle to the nearest degree.

(Note: Since the diagram for 9 and 10 is not fully detailed, we assume 10 is a right angle (90°), and 9 is an acute or obtuse angle. For drawing angles, we use a protractor method.)

Problem 11: Draw a \( 105^\circ \) angle

Step 1: Draw a ray

Draw a straight ray (one side of the angle) with a vertex at the endpoint.

Step 2: Align protractor

Place the center of the protractor on the vertex, aligning the base line with the ray.

Step 3: Mark \( 105^\circ \)

Find \( 105^\circ \) on the protractor (between \( 90^\circ \) and \( 180^\circ \)) and mark a point.

Step 4: Draw the second ray

Draw a ray from the vertex through the marked point. This forms a \( 105^\circ \) angle.

Problem 12: Draw a \( 135^\circ \) angle

Step 1: Draw a ray

Draw a straight ray (one side of the angle) with a vertex at the endpoint.

Step 2: Align protractor

Place the center of the protractor on the vertex, aligning the base line with the ray.

Step 3: Mark \( 135^\circ \)

Find \( 135^\circ \) on the protractor (between \( 90^\circ \) and \( 180^\circ \)) and mark a point.

Step 4: Draw the second ray

Draw a ray from the vertex through the marked point. This forms a \( 135^\circ \) angle.

For Angle Measurement (Problems 9–10):

If using a protractor:

• Align the protractor’s center with the angle’s vertex.
• Align the protractor’s base line with one side of the angle.
• Read the degree measure where the other side intersects the protractor. Round to the nearest degree.

(Note: Since the diagram for 9 is not labeled with side lengths or coordinates, the exact measure depends on the diagram. For 10, the angle is labeled \( 90^\circ \), so its measure is \( 90^\circ \).)

Final Answers (for labeled/marked angles):

• Problem 10: \( \boldsymbol{90^\circ} \)
• Problem 11: Drawn \( 105^\circ \) angle (as per steps).
• Problem 12: Drawn \( 135^\circ \) angle (as per steps).

(For Problem 9, measure with a protractor and round to the nearest degree.)

Answer:

Step 1: Draw a ray

Draw a straight ray (one side of the angle) with a vertex at the endpoint.

Step 2: Align protractor

Place the center of the protractor on the vertex, aligning the base line with the ray.

Step 3: Mark \( 135^\circ \)

Find \( 135^\circ \) on the protractor (between \( 90^\circ \) and \( 180^\circ \)) and mark a point.

Step 4: Draw the second ray

Draw a ray from the vertex through the marked point. This forms a \( 135^\circ \) angle.

For Angle Measurement (Problems 9–10):

If using a protractor:

• Align the protractor’s center with the angle’s vertex.
• Align the protractor’s base line with one side of the angle.
• Read the degree measure where the other side intersects the protractor. Round to the nearest degree.

(Note: Since the diagram for 9 is not labeled with side lengths or coordinates, the exact measure depends on the diagram. For 10, the angle is labeled \( 90^\circ \), so its measure is \( 90^\circ \).)

Final Answers (for labeled/marked angles):

• Problem 10: \( \boldsymbol{90^\circ} \)
• Problem 11: Drawn \( 105^\circ \) angle (as per steps).
• Problem 12: Drawn \( 135^\circ \) angle (as per steps).

(For Problem 9, measure with a protractor and round to the nearest degree.)