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Is the sum of external angle and sum of internal angle is same?
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Is the sum of external angle and sum of internal angle is same?
Understanding Internal and External Angles
The internal and external angles of a polygon are fundamental concepts in geometry. To clarify their relationship, let’s delve into their definitions and properties.
Internal Angles
- The internal angle is formed between two adjacent sides of a polygon.
- For a polygon with n sides, the sum of internal angles can be calculated using the formula: (n-2) × 180 degrees.
- For example, in a triangle (3 sides), the internal angles sum up to 180 degrees.
External Angles
- An external angle is formed by one side of the polygon and the extension of an adjacent side.
- The sum of all external angles of any polygon, regardless of the number of sides, is always 360 degrees.
- Each external angle is supplementary to its corresponding internal angle (they add up to 180 degrees).
Relationship Between Internal and External Angles
- While the sum of internal angles increases with the number of sides, the sum of external angles remains constant at 360 degrees.
- For each vertex, the internal angle plus the external angle equals 180 degrees, indicating they are related but distinct.
Conclusion
- The sum of internal angles varies based on the polygon's number of sides, while the sum of external angles is always 360 degrees.
- Therefore, the sum of external angles and the sum of internal angles are not the same; they serve different purposes in polygon geometry.
Understanding these concepts is crucial for solving problems in geometry, especially in competitive exams like UPSC.
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Accountability, or the lack of it, in governance generally, and civil services, in particular, is a major factor underlying the deficiencies in governance and public administration. Designing an effective framework for accountability has been a key element of the reform agenda. A fundamental issue is whether civil services should be accountable to the political executive of the day or to society at large. In other words, how should internal and external accountability be reconciled? Internal accountability is sought to be achieved by internal performance monitoring, official supervision by bodies like the —Central-Vigilance Commission-andComptroller and Auditor—General, and judicial review of executive decisions. Articles 311 and 312 of the Indian Constitution provide job security and safeguards to the civil services, especially the All India Services. The framers of the Constitution had envisaged that provision of these safeguards would result in a civil service that is not totally subservient to the political executive but will have the strength to function in larger public interest. The need to balance internal and external accountability is thus built into the Constitution. The issue is where to draw the line. Over the years, the emphasis seems to have tilted in favour of greater internal accountability of the civil services to the political leaders of the day who in turn are expected to be externally accountable to the society at large through the election process. This system for seeking accountability to Society has not worked out, and has led to several adverse consequences for governance.Some special measures can be considered for improving accountability in civil services.Provisions of articles 311 and 312 should be reviewed and laws and regulations framed to ensure external accountability of civil services. The proposed Civil Services Bill seeks to address some of these requirements. The respective roles of professional civil services and the political executive should he defined so that professional managerial functions and management of civil services are depoliticized. For this purpose, effective statutory civil service boards should be created at the centre and in the states. Decentralization and devolution of authority to bring government and decision making closer to the people also helps to enhance accountability.Q. According to the passage, which of the following factor/factors led to the adverse consequences for governance/public administration?1. Inability of civil services to strike a balance between internal and external accountabilities2. Lack of sufficient professional training to the officers of All India Services 3. Lack of proper service benefits in civil services4. Lack of Constitutional provisions to define the respective roles of professional civil services vis-a-vis political executive in this context Select the correct answer using the code given below

Accountability, or the lack of it, in governance generally, and civil services, in particular, is a major factor underlying the deficiencies in governance and public administration. Designing an effective framework for accountability has been a key element of the reform agenda. A fundamental issue is whether civil services should be accountable to the political executive of the day or to society at large. In other words, how should internal and external accountability be reconciled? Internal accountability is sought to be achieved by internal performance monitoring, official supervision by bodies like the —Central-Vigilance Commission-andComptroller and Auditor—General, and judicial review of executive decisions. Articles 311 and 312 of the Indian Constitution provide job security and safeguards to the civil services, especially the All India Services. The framers of the Constitution had envisaged that provision of these safeguards would result in a civil service that is not totally subservient to the political executive but will have the strength to function in larger public interest. The need to balance internal and external accountability is thus built into the Constitution. The issue is where to draw the line. Over the years, the emphasis seems to have tilted in favour of greater internal accountability of the civil services to the political leaders of the day who in turn are expected to be externally accountable to the society at large through the election process. This system for seeking accountability to Society has not worked out, and has led to several adverse consequences for governance.Some special measures can be considered for improving accountability in civil services.Provisions of articles 311 and 312 should be reviewed and laws and regulations framed to ensure external accountability of civil services. The proposed Civil Services Bill seeks to address some of these requirements. The respective roles of professional civil services and the political executive should he defined so that professional managerial functions and management of civil services are depoliticized. For this purpose, effective statutory civil service boards should be created at the centre and in the states. Decentralization and devolution of authority to bring government and decision making closer to the people also helps to enhance accountability.Q. Which one of the following is the essential message implied by this passage?

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Is the sum of external angle and sum of internal angle is same?
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Is the sum of external angle and sum of internal angle is same? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Is the sum of external angle and sum of internal angle is same? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is the sum of external angle and sum of internal angle is same?.
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