Math / Geometry

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Find the angle of rotation for the rotation that is the composition $r_{n} \circ r_{m}$ . Then, draw the image.
The angle of rotation is $\square$ $]^{\circ}$ . (Simplify your answer.) Clear all Check answer Video Textbook Get more help -

Studdy Solution

STEP 1

1. We are dealing with a composition of two rotations, $r_n$ and $r_m$ .
2. The angle between lines $n$ and $m$ is $78^\circ$ in both directions.
3. The composition of rotations is performed in the order $r_n \circ r_m$ (meaning $r_m$ is applied first, then $r_n$ ).

STEP 2

1. Understand the concept of rotation composition
2. Determine the individual rotation angles
3. Calculate the composite rotation angle
4. Simplify and present the final answer

STEP 3

In geometry, when we compose two rotations around the same center, the result is equivalent to a single rotation. The angle of this resulting rotation is the sum of the angles of the individual rotations.

STEP 4

From the diagram, we can see that the angle between lines $n$ and $m$ is $78^\circ$ . This means: - Rotation $r_m$ has an angle of $78^\circ$ - Rotation $r_n$ also has an angle of $78^\circ$

STEP 5

To find the angle of the composite rotation $r_n \circ r_m$ , we add the angles of the individual rotations:
$78^\circ + 78^\circ = 156^\circ$

STEP 6

The final answer is already in its simplest form. Therefore, the angle of rotation for the composition $r_n \circ r_m$ is $156^\circ$ .
The angle of rotation for the composition $r_n \circ r_m$ is:
$\boxed{156^\circ}$
Note: Drawing the image of the rotated triangle would require more information about the original position of the triangle and the center of rotation. Based on the given information, we can only determine the angle of rotation, not the specific image of the rotated triangle.

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Studdy Solution

STEP 1

1. We are dealing with a composition of two rotations, $r_n$ and $r_m$ .
2. The angle between lines $n$ and $m$ is $78^\circ$ in both directions.
3. The composition of rotations is performed in the order $r_n \circ r_m$ (meaning $r_m$ is applied first, then $r_n$ ).

STEP 2

1. Understand the concept of rotation composition
2. Determine the individual rotation angles
3. Calculate the composite rotation angle
4. Simplify and present the final answer

STEP 3

In geometry, when we compose two rotations around the same center, the result is equivalent to a single rotation. The angle of this resulting rotation is the sum of the angles of the individual rotations.

STEP 4

From the diagram, we can see that the angle between lines $n$ and $m$ is $78^\circ$ . This means: - Rotation $r_m$ has an angle of $78^\circ$ - Rotation $r_n$ also has an angle of $78^\circ$

STEP 5

To find the angle of the composite rotation $r_n \circ r_m$ , we add the angles of the individual rotations:
$78^\circ + 78^\circ = 156^\circ$

STEP 6

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Studdy Solution

STEP 1

STEP 2

1. Understand the concept of rotation composition2. Determine the individual rotation angles3. Calculate the composite rotation angle4. Simplify and present the final answer

STEP 3

In geometry, when we compose two rotations around the same center, the result is equivalent to a single rotation. The angle of this resulting rotation is the sum of the angles of the individual rotations.

STEP 4

From the diagram, we can see that the angle between lines nnn and mmm is 78∘78^\circ78∘. This means: - Rotation rmr_mrm​ has an angle of 78∘78^\circ78∘ - Rotation rnr_nrn​ also has an angle of 78∘78^\circ78∘

STEP 5

To find the angle of the composite rotation rn∘rmr_n \circ r_mrn​∘rm​, we add the angles of the individual rotations:78∘+78∘=156∘ 78^\circ + 78^\circ = 156^\circ 78∘+78∘=156∘

STEP 6

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Understand the concept of rotation composition
2. Determine the individual rotation angles
3. Calculate the composite rotation angle
4. Simplify and present the final answer

From the diagram, we can see that the angle between lines $n$ and $m$ is $78^\circ$ . This means: - Rotation $r_m$ has an angle of $78^\circ$ - Rotation $r_n$ also has an angle of $78^\circ$

To find the angle of the composite rotation $r_n \circ r_m$ , we add the angles of the individual rotations:
$78^\circ + 78^\circ = 156^\circ$