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Finding the Measure of Angles in Polygons

Finding the Measure of Angles in Polygons. In a regular polygon, all the angles and sides are the same size. To find the measure of a single angle: Divide the Sum by the Number of Sides. For example:

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Finding the Measure of Angles in Polygons

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  1. Finding the Measure of Angles in Polygons

  2. In a regular polygon, all the angles and sides are the same size. To find the measure of a single angle: Divide the Sum by the Number of Sides. For example: In a regular pentagon, the sum of the interior angles is 540 and the number of sides is 5. °

  3. In your notebooks:Find the measure of a single angle in each regular polygon. 180 720 360 To find the measure of a single angle: Divide the Sum of the Interior Angles by the Number of Sides/Angles.

  4. To Find the Missing Angle, with an irregular polygon: Step 1: Find the sum of the interior angles for the polygon (count number of sides, and use formula) Step 2: Add up all the given angles. Step 3: Set two sums equal to each other. Step 4: Solve for x

  5. To Find the Missing Angle: 2 135 1 x Step 1: Find the sum of the interior angles for the polygon (ignore given angles, count number of sides, and use formula) 180(n – 2) = 180(7 – 2) = 180(5) = 900° 3 90 100 7 145 4 95 170 6 5

  6. To Find the Missing Angle: 135 x Step 2: Add up all the given angles. 100 + 95 + 170 + 145 + 90 + 135 + x = 735 + x 90 100 145 95 170

  7. To Find the Missing Angle: 135 x Step 3: Set two sums equal to each other. Step 4: Solve for x (you will need to subtract) 735 + x = 900 -735 -735 x = 165° 90 100 145 95 170

  8. Practice with One Angle in Regular and Irregular Polygons • Each of you will be working on a mini-worksheet titled: “Find the Measure on One Angle in a Regular Polygon.” • Use the first part of the notes. • When you finish, there will be a worksheet up front called, “Angles and Polygons: C.” • This worksheet is practice for IRREGULAR polygons. • Use the second part of the notes. • BOTH are DUE in class.

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