ChapterP: Prerequisites
SectionP.6: The Rectangular Coordinate System And Graphs
Problem 37E: An airplane flies from Naples, Italy, in a straight line to Rome, Italy, which is 120 kilometers...
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![### Problem Statement
**Given:**
- The measure of angle \( A (m∠A) \) is 110 degrees.
- The measure of angle \( B (m∠B) \) is 35 degrees.
**Task:**
Find the measure of angle 1 (\( m∠1 \)).
- Instructions: Put just the number.
### Diagram Explanation
The provided diagram illustrates a triangle \( ABC \) with the following characteristics:
- Vertex \( A \) is at the top of the triangle.
- Vertices \( B \) and \( C \) form the base of the triangle.
- Angle \( 1 \) is an exterior angle at vertex \( C \).
### Steps to Solve:
1. **Use the Triangle Angle Sum Property:**
The sum of the interior angles of a triangle is always equal to 180 degrees.
\[ m∠A + m∠B + m∠C = 180^\circ \]
2. **Substitute the Given Values:**
\[ 110^\circ + 35^\circ + m∠C = 180^\circ \]
3. **Solve for \( m∠C \):**
\[ m∠C = 180^\circ - 110^\circ - 35^\circ \]
\[ m∠C = 35^\circ \]
4. **Exterior Angle Theorem:**
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
Therefore, \( m∠1 = m∠A + m∠B \)
5. **Calculate \( m∠1 \):**
\[ m∠1 = 110^\circ + 35^\circ \]
\[ m∠1 = 145^\circ \]
### Answer:
\[ 145 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28bd164b-15c0-4281-9396-dc8e872bf440%2F76a63d2f-5a5f-49a2-9833-3bfb7e20c241%2F5t104z9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**Given:**
- The measure of angle \( A (m∠A) \) is 110 degrees.
- The measure of angle \( B (m∠B) \) is 35 degrees.
**Task:**
Find the measure of angle 1 (\( m∠1 \)).
- Instructions: Put just the number.
### Diagram Explanation
The provided diagram illustrates a triangle \( ABC \) with the following characteristics:
- Vertex \( A \) is at the top of the triangle.
- Vertices \( B \) and \( C \) form the base of the triangle.
- Angle \( 1 \) is an exterior angle at vertex \( C \).
### Steps to Solve:
1. **Use the Triangle Angle Sum Property:**
The sum of the interior angles of a triangle is always equal to 180 degrees.
\[ m∠A + m∠B + m∠C = 180^\circ \]
2. **Substitute the Given Values:**
\[ 110^\circ + 35^\circ + m∠C = 180^\circ \]
3. **Solve for \( m∠C \):**
\[ m∠C = 180^\circ - 110^\circ - 35^\circ \]
\[ m∠C = 35^\circ \]
4. **Exterior Angle Theorem:**
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
Therefore, \( m∠1 = m∠A + m∠B \)
5. **Calculate \( m∠1 \):**
\[ m∠1 = 110^\circ + 35^\circ \]
\[ m∠1 = 145^\circ \]
### Answer:
\[ 145 \]
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