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Exploring the fundamentals of angle measurement, this overview covers techniques using a protractor, mathematical calculations for unknown angles, and trigonometry in right-angled triangles. It delves into the units of measurement for angles, such as degrees and radians, and provides insights into calculating acute angles and the sum of interior angles in polygons. The content is essential for understanding geometric principles and their applications in various problems.

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## Definition and Importance of Angle Measurement

### Angle Measurement Techniques

Angle measurement is achieved through various techniques, including the use of a protractor and mathematical calculations

### Applications of Angle Measurement

Calculating Unknown Angles

Unknown angles can be calculated using geometric principles and formulas, such as the sum of angles on a straight line and the sum of interior angles in polygons

Trigonometry and Right-Angled Triangles

Trigonometry is useful in analyzing right-angled triangles and determining relationships between angles and side lengths

### Units of Angle Measurement

Angles can be measured in degrees and radians, with radians being commonly used in advanced mathematics and physics

## Angle Measurement Techniques

### Using a Protractor

A protractor is a semi-circular instrument marked with degrees that can be used to measure angles by aligning its midpoint with the vertex and one ray with the baseline

### Mathematical Calculations

Sum of Angles on a Straight Line

The sum of angles on a straight line is 180 degrees, allowing for the calculation of unknown angles

Sum of Interior Angles in Polygons

The sum of interior angles in a polygon can be found using the formula (n-2)×180°, where 'n' is the number of sides

### Trigonometric Calculations

Trigonometric ratios and inverse trigonometric functions can be used to find unknown angles in right-angled triangles

## Units of Angle Measurement

### Degrees

A degree is a measure that divides one full rotation into 360 equal parts

### Radians

A radian is a measure where one full rotation is equal to 2π radians, commonly used in advanced mathematics and physics

### Converting Between Degrees and Radians

Degrees can be converted to radians using the formula Radians = Degrees × π/180

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