A Polygon Has 6 Sides How Would I Find The Measure Class 10 Maths ...

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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsA polygon has 6 sides. How would I find the measure of each exterior and interior angle? AnswerVerified566.4k+ viewsHint: We recall definitions of interior angle and exterior angle of a polygon. We can only find all measures of all interior and exterior angles if the polygon is regular. We recall that interior angle of a regular polygon is $\dfrac{{{180}^{\circ }}\left( n-2 \right)}{n}$ and measure of exterior angle as ${{180}^{\circ }}-\dfrac{{{180}^{\circ }}\left( n-2 \right)}{n}$. We use these formulas for $n=6$.\[\]Complete step by step answer:We know from geometry that a polygon closed and simple curve which is made up of joining distinct points by line segments. Those points are called vertices and those line segments are called sides. If the length of all sides is equal, then we call the polygon regular polygon. \[\]We also know that the angle subtended by two sides of a polygon in the interior of the polygon and angle subtended in the exterior of the polygon by side and its adjacent extended side extended is called exterior angle. We show an interior and exterior angle of a regular polygon with 6 sides .\[\] We see above the interior angle $\angle ABC$ and from sides $AB,AC$ and exterior angle $\angle ABP$ made by side with side $CB$ extended to $\overrightarrow{CP}$. \[\]We know from angle sum property that the sum of interior angles of as ${{180}^{\circ }}\left( n-2 \right)$ and measure of all angles in a regular polygon is equal. So the measure of one interior angle is $\dfrac{{{180}^{\circ }}\left( n-2 \right)}{n}$. Since exterior and interior angles are supplementary to each other (like here $\angle ABC+\angle ABP={{180}^{\circ }}$ ) we have measure of one exterior angle as ${{180}^{\circ }}-\dfrac{{{180}^{\circ }}\left( n-2 \right)}{n}$. \[\]We are given there are 6 sides. If the polygon is regular then measure of one interior angle is \[\dfrac{{{180}^{\circ }}\left( n-2 \right)}{n}=\dfrac{{{180}^{\circ }}\left( 6-2 \right)}{6}=\dfrac{{{180}^{\circ }}\times 4}{6}={{30}^{\circ }}\times 4={{120}^{\circ }}\]Then the measure of one exterior angle is \[{{180}^{\circ }}-\dfrac{{{180}^{\circ }}\left( n-2 \right)}{n}={{180}^{\circ }}-{{120}^{\circ }}={{60}^{\circ }}\]Note: We note that if there are $n$ sides of a polygon then there are $n$ interior and $2n$ exterior angles. If we move from one vertex to another we shall meet $n$ exterior angles in one revolution. By exterior angle sum theorem their sum is ${{360}^{\circ }}$. So we can find alternatively the measure of one exterior angle as $\dfrac{{{360}^{\circ }}}{n}=\dfrac{{{360}^{\circ }}}{6}={{60}^{\circ }}$.Recently Updated PagesClass 10 Question and Answer - Your Ultimate Solutions GuideMaster Class 10 General Knowledge: Engaging Questions & Answers for SuccessMaster Class 10 Social Science: Engaging Questions & Answers for SuccessMaster Class 10 Computer Science: Engaging Questions & Answers for SuccessMaster Class 10 Maths: Engaging Questions & Answers for SuccessMaster Class 10 Science: Engaging Questions & Answers for SuccessClass 10 Question and Answer - Your Ultimate Solutions GuideMaster Class 10 General Knowledge: Engaging Questions & Answers for SuccessMaster Class 10 Social Science: Engaging Questions & Answers for SuccessMaster Class 10 Computer Science: Engaging Questions & Answers for SuccessMaster Class 10 Maths: Engaging Questions & Answers for SuccessMaster Class 10 Science: Engaging Questions & Answers for Success

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