Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
ChapterCSR: Contents Of Student Resources
Section: Chapter Questions
Problem 1.41EP
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Question
![### Find the Measure of the Missing Angles
Below is a diagram of intersecting lines forming multiple angles. Given angles \(23^\circ\) and \(84^\circ\) are labeled, and we need to determine the measures of the missing angles \(d\), \(e\), and \(f\).
#### Diagram Description
The diagram shows two pairs of intersecting lines, creating various angles at the intersection point. The angles are labeled as follows:
- The top part of the vertical line intersects with an angle of \(23^\circ\).
- The bottom left part of the vertical line intersects with an angle of \(84^\circ\).
- The angles \(d\), \(e\), and \(f\) need to be determined:
- Angle \(d\) is opposite to the \(84^\circ\) angle.
- Angle \(e\) is adjacent to the \(23^\circ\) angle.
- Angle \(f\) is adjacent to the \(84^\circ\) angle and supplementary to \(e\).
#### Submitting the Answer
There are three fields where you can input the values of \(d\), \(e\), and \(f\):
\[
d = \ \ \ \ \ \ ^\circ
\]
\[
e = \ \ \ \ \ \ ^\circ
\]
\[
f = \ \ \ \ \ \ ^\circ
\]
Press the "Submit Answer" button when you are done.
For reference:
- Vertical angles are equal.
- Adjacent angles on a straight line sum up to \(180^\circ\).
### Example Calculation:
1. \(d\) is the vertical angle to \(84^\circ\):
\[ d = 84^\circ \]
2. \(e\) and \(23^\circ\) are adjacent and supplementary:
\[ e + 23^\circ = 180^\circ \]
\[ e = 180^\circ - 23^\circ \]
\[ e = 157^\circ \]
3. \(f\) is the vertical angle to \(e\):
\[ f = 157^\circ \]
You can now fill in the blanks and check your answers.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F55768b86-6bfe-4eb3-a58c-b2ce70ea7705%2F68d2dbbd-a577-4330-958f-740f9e08a7a6%2Fqnrtpsm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Find the Measure of the Missing Angles
Below is a diagram of intersecting lines forming multiple angles. Given angles \(23^\circ\) and \(84^\circ\) are labeled, and we need to determine the measures of the missing angles \(d\), \(e\), and \(f\).
#### Diagram Description
The diagram shows two pairs of intersecting lines, creating various angles at the intersection point. The angles are labeled as follows:
- The top part of the vertical line intersects with an angle of \(23^\circ\).
- The bottom left part of the vertical line intersects with an angle of \(84^\circ\).
- The angles \(d\), \(e\), and \(f\) need to be determined:
- Angle \(d\) is opposite to the \(84^\circ\) angle.
- Angle \(e\) is adjacent to the \(23^\circ\) angle.
- Angle \(f\) is adjacent to the \(84^\circ\) angle and supplementary to \(e\).
#### Submitting the Answer
There are three fields where you can input the values of \(d\), \(e\), and \(f\):
\[
d = \ \ \ \ \ \ ^\circ
\]
\[
e = \ \ \ \ \ \ ^\circ
\]
\[
f = \ \ \ \ \ \ ^\circ
\]
Press the "Submit Answer" button when you are done.
For reference:
- Vertical angles are equal.
- Adjacent angles on a straight line sum up to \(180^\circ\).
### Example Calculation:
1. \(d\) is the vertical angle to \(84^\circ\):
\[ d = 84^\circ \]
2. \(e\) and \(23^\circ\) are adjacent and supplementary:
\[ e + 23^\circ = 180^\circ \]
\[ e = 180^\circ - 23^\circ \]
\[ e = 157^\circ \]
3. \(f\) is the vertical angle to \(e\):
\[ f = 157^\circ \]
You can now fill in the blanks and check your answers.
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