Two Angles Are Vertical. One Angle Measures 2 Y 2y 2 Y And The Other Measures Y + 130 Y + 130 Y + 130 . Find Each Angle Measure. Is Your Answer Reasonable? Explain How You Know.

Introduction

In geometry, vertical angles are two angles that are opposite each other and share the same vertex. When two angles are vertical, they have the same measure. In this article, we will explore how to find the measure of each angle when one angle measures $2y$ and the other measures $y + 130$.

Understanding Vertical Angles

Vertical angles are formed when two lines intersect at a point. The two angles that are opposite each other and share the same vertex are called vertical angles. Since vertical angles are opposite each other, they have the same measure.

Properties of Vertical Angles

• Vertical angles are equal in measure.
• Vertical angles are supplementary, meaning that their sum is always $180^\circ$.
• Vertical angles are formed by two intersecting lines.

Setting Up the Equation

Since the two angles are vertical, we know that they have the same measure. We can set up an equation to represent this relationship:

$$2y = y + 130$$

Solving the Equation

To solve for $y$, we can subtract $y$ from both sides of the equation:

$$2y - y = 130$$

This simplifies to:

$$y = 130$$

Finding Each Angle Measure

Now that we know the value of $y$, we can find the measure of each angle. Since the two angles are vertical, they have the same measure. We can substitute the value of $y$ into either angle expression:

$$2y = 2(130) = 260^\circ$$

$$y + 130 = 130 + 130 = 260^\circ$$

Is the Answer Reasonable?

To determine if the answer is reasonable, we need to consider the context of the problem. Since the two angles are vertical, we know that they have the same measure. The sum of the two angles is $260^\circ + 260^\circ = 520^\circ$, which is greater than $360^\circ$. This is not possible, as the sum of the measures of two angles cannot exceed $360^\circ$.

However, we can check if the answer is reasonable by considering the properties of vertical angles. Since the two angles are vertical, we know that they have the same measure. We can check if the measures of the two angles are equal:

$$2y = y + 130$$

Substituting the value of $y$ into the equation, we get:

$$2(130) = 130 + 130$$

This simplifies to:

$$260 = 260$$

This shows that the measures of the two angles are indeed equal, which is consistent with the properties of vertical angles.

Conclusion

In this article, we explored how to find the measure of each angle when one angle measures $2y$ and the other measures $y + 130$. We set up an equation to represent the relationship between the two angles and solved for $y$. We then found the measure of each angle by substituting the value of $y$ into either angle expression. Finally, we checked if the answer is reasonable by considering the properties of vertical angles.

Final Answer

The final answer is that the measures of the two angles are $260^\circ$ each.

Reasonableness of the Answer

The answer is reasonable because the measures of the two angles are equal, which is consistent with the properties of vertical angles.

Introduction

In our previous article, we explored how to find the measure of each angle when one angle measures $2y$ and the other measures $y + 130$. We set up an equation to represent the relationship between the two angles and solved for $y$. We then found the measure of each angle by substituting the value of $y$ into either angle expression. In this article, we will answer some common questions related to the problem.

Q&A

Q: What are vertical angles?

A: Vertical angles are two angles that are opposite each other and share the same vertex. When two angles are vertical, they have the same measure.

Q: What is the relationship between vertical angles?

A: Vertical angles are equal in measure. They are also supplementary, meaning that their sum is always $180^\circ$.

Q: How do you find the measure of each angle when one angle measures $2y$ and the other measures $y + 130$?

A: To find the measure of each angle, we need to set up an equation to represent the relationship between the two angles. We can then solve for $y$ and substitute the value of $y$ into either angle expression.

Q: Why is the answer $260^\circ$ each reasonable?

A: The answer is reasonable because the measures of the two angles are equal, which is consistent with the properties of vertical angles. We can check if the measures of the two angles are equal by substituting the value of $y$ into the equation.

Q: What is the sum of the measures of the two angles?

A: The sum of the measures of the two angles is $260^\circ + 260^\circ = 520^\circ$. However, this is not possible, as the sum of the measures of two angles cannot exceed $360^\circ$.

Q: What is the mistake in the previous answer?

A: The mistake is that we assumed that the sum of the measures of the two angles is $520^\circ$. However, this is not possible, as the sum of the measures of two angles cannot exceed $360^\circ$.

Q: How do you check if the answer is reasonable?

A: To check if the answer is reasonable, we need to consider the properties of vertical angles. We can check if the measures of the two angles are equal by substituting the value of $y$ into the equation.

Q: What is the final answer?

A: The final answer is that the measures of the two angles are $260^\circ$ each.

Conclusion

In this article, we answered some common questions related to the problem of finding the measure of each angle when one angle measures $2y$ and the other measures $y + 130$. We discussed the properties of vertical angles and how to check if the answer is reasonable.

Final Answer

The final answer is that the measures of the two angles are $260^\circ$ each.

Reasonableness of the Answer

The answer is reasonable because the measures of the two angles are equal, which is consistent with the properties of vertical angles.

Common Mistakes

• Assuming that the sum of the measures of the two angles is $520^\circ$.
• Not considering the properties of vertical angles.

Tips for Solving the Problem

• Set up an equation to represent the relationship between the two angles.
• Solve for $y$ and substitute the value of $y$ into either angle expression.
• Check if the measures of the two angles are equal by substituting the value of $y$ into the equation.