Suppose That You Know That \[$\angle T\$\] And \[$\angle S\$\] Are Supplementary, And That \[$m \angle T = 7 \cdot (m \angle S)\$\]. Complete The Explanation For How You Can Find \[$m \angle T\$\]. Let \[$m \angle S

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Understanding Supplementary Angles

In geometry, supplementary angles are two angles whose measures add up to 180 degrees. This concept is crucial in solving various problems involving angles. In this article, we will explore how to find the measure of one supplementary angle when the measure of the other angle is known, and the relationship between the two angles is given.

The Relationship Between Supplementary Angles

Given that {\angle T$}$ and {\angle S$}$ are supplementary, we can express this relationship as:

m∠T+m∠S=180∘m \angle T + m \angle S = 180^\circ

The Relationship Between the Measures of the Angles

We are also given that {m \angle T = 7 \cdot (m \angle S)$}$. This relationship can be expressed as:

m∠T=7m∠Sm \angle T = 7m \angle S

Substituting the Relationship into the Equation

We can substitute the relationship between the measures of the angles into the equation for supplementary angles:

7m∠S+m∠S=180∘7m \angle S + m \angle S = 180^\circ

Combining Like Terms

We can combine like terms in the equation:

8m∠S=180∘8m \angle S = 180^\circ

Solving for {m \angle S$}$

To solve for {m \angle S$}$, we can divide both sides of the equation by 8:

m∠S=180∘8m \angle S = \frac{180^\circ}{8}

Calculating the Measure of {m \angle S$}$

We can calculate the measure of {m \angle S$}$ as:

m∠S=22.5∘m \angle S = 22.5^\circ

Finding the Measure of {m \angle T$}$

Now that we have found the measure of {m \angle S$}$, we can use the relationship between the measures of the angles to find the measure of {m \angle T$}$:

m∠T=7m∠Sm \angle T = 7m \angle S

Calculating the Measure of {m \angle T$}$

We can calculate the measure of {m \angle T$}$ as:

m∠T=7⋅22.5∘m \angle T = 7 \cdot 22.5^\circ

Final Calculation

We can calculate the final value of {m \angle T$}$ as:

m∠T=157.5∘m \angle T = 157.5^\circ

Conclusion

In this article, we have explored how to find the measure of one supplementary angle when the measure of the other angle is known, and the relationship between the two angles is given. We have used the concept of supplementary angles and the relationship between the measures of the angles to solve for the measure of {m \angle T$}$. The final answer is ${157.5^\circ\$}.

Additional Information

  • Supplementary angles are two angles whose measures add up to 180 degrees.
  • The relationship between the measures of supplementary angles can be expressed as {m \angle T + m \angle S = 180^\circ$}$.
  • The relationship between the measures of the angles can be expressed as {m \angle T = 7 \cdot (m \angle S)$}$.
  • To find the measure of one supplementary angle, we can use the relationship between the measures of the angles and the equation for supplementary angles.

References

Frequently Asked Questions

  • What are supplementary angles?
    • Supplementary angles are two angles whose measures add up to 180 degrees.
  • How do I find the measure of one supplementary angle when the measure of the other angle is known?
    • You can use the relationship between the measures of the angles and the equation for supplementary angles to solve for the measure of the angle.
  • What is the relationship between the measures of supplementary angles?
    • The relationship between the measures of supplementary angles can be expressed as {m \angle T + m \angle S = 180^\circ$}$.
      Supplementary Angles Q&A ==========================

Frequently Asked Questions

Q: What are supplementary angles?

A: Supplementary angles are two angles whose measures add up to 180 degrees.

Q: How do I find the measure of one supplementary angle when the measure of the other angle is known?

A: To find the measure of one supplementary angle, you can use the relationship between the measures of the angles and the equation for supplementary angles. If you know the measure of one angle, you can set up an equation using the relationship between the measures of the angles and solve for the measure of the other angle.

Q: What is the relationship between the measures of supplementary angles?

A: The relationship between the measures of supplementary angles can be expressed as:

m∠T+m∠S=180∘m \angle T + m \angle S = 180^\circ

Q: How do I use the relationship between the measures of the angles to find the measure of one supplementary angle?

A: To use the relationship between the measures of the angles to find the measure of one supplementary angle, you can substitute the relationship into the equation for supplementary angles and solve for the measure of the angle.

Q: What is the formula for finding the measure of one supplementary angle?

A: The formula for finding the measure of one supplementary angle is:

m∠T=7m∠Sm \angle T = 7m \angle S

Q: How do I calculate the measure of one supplementary angle using the formula?

A: To calculate the measure of one supplementary angle using the formula, you can substitute the measure of the other angle into the formula and solve for the measure of the angle.

Q: What are some examples of supplementary angles?

A: Some examples of supplementary angles include:

  • 90° and 90°
  • 60° and 120°
  • 30° and 150°

Q: How do I determine if two angles are supplementary?

A: To determine if two angles are supplementary, you can add their measures together and check if the sum is equal to 180°.

Q: What are some real-world applications of supplementary angles?

A: Some real-world applications of supplementary angles include:

  • Architecture: Supplementary angles are used in the design of buildings and bridges to ensure that the angles of the structures are correct.
  • Engineering: Supplementary angles are used in the design of machines and mechanisms to ensure that the angles of the components are correct.
  • Art: Supplementary angles are used in the creation of art to create balanced and harmonious compositions.

Q: How do I use supplementary angles in geometry?

A: To use supplementary angles in geometry, you can use the relationship between the measures of the angles to solve for the measure of one angle. You can also use supplementary angles to create balanced and harmonious compositions in art.

Q: What are some common mistakes to avoid when working with supplementary angles?

A: Some common mistakes to avoid when working with supplementary angles include:

  • Not using the correct formula for finding the measure of one supplementary angle.
  • Not substituting the relationship between the measures of the angles into the equation for supplementary angles.
  • Not solving for the measure of the angle correctly.

Q: How do I practice working with supplementary angles?

A: To practice working with supplementary angles, you can try the following:

  • Use online resources to practice solving problems involving supplementary angles.
  • Work with a partner or tutor to practice solving problems involving supplementary angles.
  • Use real-world examples to practice applying supplementary angles in different contexts.

Conclusion

In this article, we have explored some frequently asked questions about supplementary angles. We have discussed the relationship between the measures of supplementary angles, how to find the measure of one supplementary angle, and some real-world applications of supplementary angles. We have also provided some examples and tips for practicing working with supplementary angles.