Table of Contents
Toggle$\begin{array}{r}\text{Numberofsides}(n)\end{array}$ | $\begin{array}{r}\text{Measureofallinteriorangles}\\ (n-2)\times {180}^{\circ}\end{array}$ | $\begin{array}{r}\text{Measureofeachinteriorangle}(\theta )\\ \frac{(n-2)\times {180}^{\circ}}{n}\end{array}$ |
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$\begin{array}{r}3\end{array}$ | $\begin{array}{c}(n-2)\times {180}^{\circ}\\ (3-2)\times {180}^{\circ}={180}^{\circ}\end{array}$ | $\begin{array}{r}\frac{(3-2)\times {180}^{\circ}}{3}={60}^{\circ}\end{array}$ |
$\begin{array}{r}4\end{array}$ | $\begin{array}{r}(n-2)\times {180}^{\circ}\\ \\ (4-2)\times {180}^{\circ}={360}^{\circ}\end{array}$ | $\begin{array}{r}\frac{(4-2)\times {180}^{\circ}}{4}={90}^{\circ}\end{array}$ |
$\begin{array}{r}5\end{array}$ | $\begin{array}{r}(n-2)\times {180}^{\circ}\\ (5-2)\times {180}^{\circ}={540}^{\circ}\text{}\end{array}$ | $\begin{array}{r}\frac{(5-2)\times {180}^{\circ}}{5}={108}^{\circ}\end{array}$ |
$\begin{array}{r}6\end{array}$ | $\begin{array}{r}(n-2)\times {180}^{\circ}\\ (6-2)\times {180}^{\circ}={720}^{\circ}\text{}\end{array}$ | $\begin{array}{r}\frac{(6-2)\times {180}^{\circ}}{6}={120}^{\circ}\end{array}$ |
$\begin{array}{r}\text{Numberofsides}(n)\end{array}$ | $\begin{array}{r}\text{Measureofallinteriorangles}\\ (n-2)\times {180}^{\circ}\end{array}$ | $\begin{array}{r}\text{Measureofeachinteriorangle}(\theta )\\ \frac{(n-2)\times {180}^{\circ}}{n}\end{array}$ | $\begin{array}{r}\text{Measureofeachinteriorangle}(\theta )\\ =180\xb0-\text{each exterior angle}\end{array}$ |
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$\begin{array}{r}3\end{array}$ | $\begin{array}{c}(n-2)\times {180}^{\circ}\\ (3-2)\times {180}^{\circ}={180}^{\circ}\end{array}$ | $\begin{array}{r}\frac{(3-2)\times {180}^{\circ}}{3}={60}^{\circ}\end{array}$ | $\begin{array}{r}=180\xb0-60\xb0=120\xb0\end{array}$ |
$\begin{array}{r}4\end{array}$ | $\begin{array}{r}(n-2)\times {180}^{\circ}\\ \\ (4-2)\times {180}^{\circ}={360}^{\circ}\end{array}$ | $\begin{array}{r}\frac{(4-2)\times {180}^{\circ}}{4}={90}^{\circ}\end{array}$ | $\begin{array}{r}=180\xb0-90\xb0=90\xb0\end{array}$ |
$\begin{array}{r}5\end{array}$ | $\begin{array}{r}(n-2)\times {180}^{\circ}\\ (5-2)\times {180}^{\circ}={540}^{\circ}\text{}\end{array}$ | $\begin{array}{r}\frac{(5-2)\times {180}^{\circ}}{5}={108}^{\circ}\end{array}$ | $\begin{array}{r}=180\xb0-108\xb0=72\xb0\end{array}$ |
$\begin{array}{r}6\end{array}$ | $\begin{array}{r}(n-2)\times {180}^{\circ}\\ (6-2)\times {180}^{\circ}={720}^{\circ}\text{}\end{array}$ | $\begin{array}{r}\frac{(6-2)\times {180}^{\circ}}{6}={120}^{\circ}\end{array}$ | $\begin{array}{r}=180\xb0-120\xb0=60\xb0\end{array}$ |
Calculating the measure of an exterior angle is a fundamental concept in geometry that has various practical applications across different fields. Here are some key applications:Measure Of An Exterior Angle
Designing Structures: Architects and engineers use exterior angles to design and construct buildings and other structures. For example, when creating floor plans for polygonal structures, knowing the exterior angles ensures proper alignment and stability.Measure Of An Exterior Angle
Creating Roofs and Bridges: The calculation of exterior angles is crucial in the design of roofs and bridges, especially those with polygonal shapes, to ensure that all components fit together correctly.Measure Of An Exterior Angle
Street Layouts: Urban planners use exterior angles to design street layouts and intersections. For example, when designing roundabouts or traffic circles, the angles between roads must be calculated accurately to ensure smooth traffic flow.Measure Of An Exterior Angle
Park and Garden Designs: In landscape architecture, exterior angles help in designing park layouts, garden paths, and other outdoor spaces with geometric patterns.Measure Of An Exterior Angle
Creating Geometric Art: Artists and graphic designers use exterior angles to create geometric patterns and artworks. Understanding the properties of polygons and their exterior angles helps in designing symmetrical and aesthetically pleasing pieces.Measure Of An Exterior Angle
Tiling and Mosaics: When designing tiling patterns or mosaics, the calculation of exterior angles ensures that the tiles fit together without gaps or overlaps, creating a seamless design.Measure Of An Exterior Angle
Map Making: Cartographers use the principles of exterior angles in the creation of maps and navigation charts. Accurate calculation of angles is essential for representing geographical features and plotting courses.Measure Of An Exterior Angle
Surveying: Surveyors use exterior angles to measure and map out land boundaries and construction sites. This is crucial for creating accurate property maps and ensuring legal boundaries are maintained.Measure Of An Exterior Angle
Programming Movement: In robotics, calculating exterior angles is essential for programming the movement of robots, especially those that navigate polygonal paths or need to make precise turns.Measure Of An Exterior Angle
Computer Animation: Animators use exterior angles in computer graphics to create realistic movements and rotations of objects. This is especially important in creating lifelike animations and simulations.Measure Of An Exterior Angle