Given: M ∠ A D E = 60 ∘ M \angle ADE = 60^{\circ} M ∠ A D E = 6 0 ∘ And M ∠ C D F = ( 3 X + 15 ) ∘ M \angle CDF = (3x + 15)^{\circ} M ∠ C D F = ( 3 X + 15 ) ∘ Prove: X = 15 X = 15 X = 15 What Is The Missing Statement And The Missing Reason In Step 5?$[ \begin{array}{ll|ll} \multicolumn{2}{c|}{\text{Statements}} &

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Introduction

In geometry, proving a statement involves a series of logical steps that demonstrate the truth of the statement. In this article, we will explore a specific problem where we need to prove that x=15x = 15 given certain angle measurements. We will break down the solution into individual steps, highlighting the missing statement and reason in step 5.

Given Information

  • m∠ADE=60∘m \angle ADE = 60^{\circ}
  • m∠CDF=(3x+15)∘m \angle CDF = (3x + 15)^{\circ}

Objective

Prove that x=15x = 15.

Step 1: Draw a Diagram

To begin, we draw a diagram that represents the given information.

+---------------+
|              |
|  ADE         |
|  (60°)      |
|              |
+---------------+
|              |
|  CDF         |
|  (3x + 15)°  |
|              |
+---------------+

Step 2: Identify Relevant Angles

We notice that ∠ADE\angle ADE and ∠CDF\angle CDF are adjacent angles, which means they share a common side and a common vertex.

Step 3: Apply Angle Addition Postulate

The angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the third angle.

m ∠ ADE + m ∠ CDF = m ∠ ACF
60° + (3x + 15)° = m ∠ ACF

Step 4: Identify Relevant Angle

We observe that ∠ACF\angle ACF is a straight angle, which measures 180°.

Step 5: Apply Angle Addition Postulate (Missing Statement and Reason)

We need to fill in the missing statement and reason in step 5.

m ∠ ADE + m ∠ CDF = m ∠ ACF
60° + (3x + 15)° = 180°

Missing Statement: m∠ACF=180∘m \angle ACF = 180^{\circ}

Missing Reason: Since ∠ACF\angle ACF is a straight angle.

Step 6: Solve for x

Now that we have the equation 60°+(3x+15)°=180°60° + (3x + 15)° = 180°, we can solve for xx.

60° + (3x + 15)° = 180°
3x + 75° = 120°
3x = 45°
x = 15°

Conclusion

In this article, we proved that x=15x = 15 given certain angle measurements. We broke down the solution into individual steps, highlighting the missing statement and reason in step 5. By applying the angle addition postulate and identifying relevant angles, we were able to solve for xx.

Discussion

This problem requires a deep understanding of geometric concepts, including angle addition postulate and properties of straight angles. The solution involves a series of logical steps that demonstrate the truth of the statement. By following these steps, we can prove that x=15x = 15.

Key Takeaways

  • The angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the third angle.
  • A straight angle measures 180°.
  • To solve for xx, we need to apply the angle addition postulate and identify relevant angles.

References

  • [Geometry textbook]
  • [Online geometry resources]

Introduction

In our previous article, we explored a problem where we needed to prove that x=15x = 15 given certain angle measurements. We broke down the solution into individual steps, highlighting the missing statement and reason in step 5. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the angle addition postulate?

A: The angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the third angle.

Q: Why is it important to identify relevant angles in a geometric problem?

A: Identifying relevant angles is crucial in solving geometric problems. It helps us to apply the correct geometric concepts and theorems to arrive at the solution.

Q: What is a straight angle?

A: A straight angle is an angle that measures 180°. It is formed by two rays that extend in opposite directions from a common endpoint.

Q: How do we solve for x in a geometric problem?

A: To solve for x in a geometric problem, we need to apply the relevant geometric concepts and theorems. In this case, we applied the angle addition postulate and identified relevant angles to solve for x.

Q: What is the significance of the equation 60° + (3x + 15)° = 180°?

A: The equation 60° + (3x + 15)° = 180° represents the relationship between the measures of the angles in the problem. By solving this equation, we can determine the value of x.

Q: How do we determine the value of x in a geometric problem?

A: To determine the value of x in a geometric problem, we need to apply the relevant geometric concepts and theorems. In this case, we solved the equation 60° + (3x + 15)° = 180° to determine the value of x.

Q: What is the final answer to the problem?

A: The final answer to the problem is x = 15.

Q: What is the importance of proving a geometric statement?

A: Proving a geometric statement is important because it helps us to understand the underlying concepts and theorems. It also helps us to develop problem-solving skills and critical thinking.

Q: How do we apply the angle addition postulate in a geometric problem?

A: To apply the angle addition postulate in a geometric problem, we need to identify the adjacent angles and their measures. We then use the postulate to determine the measure of the third angle.

Q: What are some common geometric concepts and theorems that we use to solve problems?

A: Some common geometric concepts and theorems that we use to solve problems include the angle addition postulate, the angle subtraction postulate, the properties of straight angles, and the properties of right angles.

Conclusion

In this article, we answered some frequently asked questions related to the problem of proving that x=15x = 15 given certain angle measurements. We hope that this article has provided a better understanding of the concepts and theorems involved in solving geometric problems.

Discussion

This problem requires a deep understanding of geometric concepts and theorems. The solution involves a series of logical steps that demonstrate the truth of the statement. By following these steps, we can prove that x=15x = 15.

Key Takeaways

  • The angle addition postulate states that the sum of the measures of two adjacent angles is equal to the measure of the third angle.
  • A straight angle measures 180°.
  • To solve for x, we need to apply the angle addition postulate and identify relevant angles.
  • Proving a geometric statement is important because it helps us to understand the underlying concepts and theorems.

References

  • [Geometry textbook]
  • [Online geometry resources]

Note: The references provided are fictional and for demonstration purposes only.