Four interior angles of a five-sided polygon traverse were observed as A = 106°4759", B = 115°06'12", C = 122°33′32", and D = 116°02′25". The angle at E was not observed. If all observed angles are assumed to be correct, what is the value of angle E? Express your answer in degrees to six significant figures.
Four interior angles of a five-sided polygon traverse were observed as A = 106°4759", B = 115°06'12", C = 122°33′32", and D = 116°02′25". The angle at E was not observed. If all observed angles are assumed to be correct, what is the value of angle E? Express your answer in degrees to six significant figures.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Four interior angles of a five-sided polygon traverse were observed as A=106∘4759", B=115∘06′12", C=122∘33′32", and D=116∘02′25". The angle at E was not observed.
![### Task: Calculating the Missing Angle in a Polygon
#### Problem Description
Four interior angles of a five-sided polygon traverse were observed as follows:
- \( A = 106^\circ 47'59'' \)
- \( B = 115^\circ 06'12'' \)
- \( C = 122^\circ 33'32'' \)
- \( D = 116^\circ 02'25'' \)
The angle at \( E \) was not observed.
#### Part A
If all observed angles are assumed to be correct, what is the value of angle \( E \)?
**Express your answer in degrees to six significant figures.**
\[ E = \]
**Instructions for Solution:**
1. Recall that the sum of the interior angles of a polygon can be calculated using the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides in the polygon.
2. For a five-sided polygon (\( n = 5 \)), the sum becomes:
\[ \text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ \]
3. To find the missing angle \( E \), subtract the sum of the known angles from the total sum.
\[
E = 540^\circ - ( A + B + C + D )
\]
Converting the given angles from degrees, minutes, and seconds to decimals may be helpful for precise calculation.
#### Provided Input:
- \( A = 106^\circ 47'59'' \rightarrow 106^\circ + \frac{47}{60}^\circ + \frac{59}{3600}^\circ \)
- \( B = 115^\circ 06'12'' \rightarrow 115^\circ + \frac{06}{60}^\circ + \frac{12}{3600}^\circ \)
- \( C = 122^\circ 33'32'' \rightarrow 122^\circ + \frac{33}{60}^\circ + \frac{32}{3600}^\circ \)
- \( D = 116^\circ 02'25'' \rightarrow 116^\circ + \frac{02}{60}^\circ + \frac](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F225ea937-ec91-4f60-983d-e6a97001b794%2Fefe4afe3-86e2-4f33-a0df-a3c9b654a299%2Ffgm8eyi_processed.png&w=3840&q=75)
Transcribed Image Text:### Task: Calculating the Missing Angle in a Polygon
#### Problem Description
Four interior angles of a five-sided polygon traverse were observed as follows:
- \( A = 106^\circ 47'59'' \)
- \( B = 115^\circ 06'12'' \)
- \( C = 122^\circ 33'32'' \)
- \( D = 116^\circ 02'25'' \)
The angle at \( E \) was not observed.
#### Part A
If all observed angles are assumed to be correct, what is the value of angle \( E \)?
**Express your answer in degrees to six significant figures.**
\[ E = \]
**Instructions for Solution:**
1. Recall that the sum of the interior angles of a polygon can be calculated using the formula:
\[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \]
where \( n \) is the number of sides in the polygon.
2. For a five-sided polygon (\( n = 5 \)), the sum becomes:
\[ \text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ \]
3. To find the missing angle \( E \), subtract the sum of the known angles from the total sum.
\[
E = 540^\circ - ( A + B + C + D )
\]
Converting the given angles from degrees, minutes, and seconds to decimals may be helpful for precise calculation.
#### Provided Input:
- \( A = 106^\circ 47'59'' \rightarrow 106^\circ + \frac{47}{60}^\circ + \frac{59}{3600}^\circ \)
- \( B = 115^\circ 06'12'' \rightarrow 115^\circ + \frac{06}{60}^\circ + \frac{12}{3600}^\circ \)
- \( C = 122^\circ 33'32'' \rightarrow 122^\circ + \frac{33}{60}^\circ + \frac{32}{3600}^\circ \)
- \( D = 116^\circ 02'25'' \rightarrow 116^\circ + \frac{02}{60}^\circ + \frac
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