Lesson 7.1 Angles of Polygons Learning Target:
Author : faustina-dinatale | Published Date : 2025-05-12
Description: Lesson 71 Angles of Polygons Learning Target Find angle measures of polygons Success Criteria I can find the sum of the interior angle measures of a polygon I can find interior angle measures of polygons I can find exterior angle
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Transcript:Lesson 7.1 Angles of Polygons Learning Target::
Lesson 7.1 Angles of Polygons Learning Target: Find angle measures of polygons. Success Criteria: I can find the sum of the interior angle measures of a polygon. I can find interior angle measures of polygons. I can find exterior angle measures of polygons. Vocabulary diagonal, p. 354 equilateral polygon, p. 356 equiangular polygon, p. 356 regular polygon, p. 356 Example 1 Finding the Sum of Angle Measures in a Polygon Find the sum of the measures of the interior angles of the figure. The figure is a convex octagon. It has 8 sides. Use the Polygon Interior Angles Theorem. Substitute 8 for n. Subtract. Multiply. SOLUTION Example 2 Finding the Number of Sides of a Polygon Use the Polygon Interior Angles Theorem to write an equation involving the number of sides n. Then solve the equation to find the number of sides. Polygon Interior Angles Theorem Add 2 to each side. SOLUTION Example 3 Finding an Unknown Interior Angle Measure Find the value of x in the diagram. The polygon is a quadrilateral. Use the Corollary to the Polygon Interior Angles Theorem to write an equation involving x. Then solve the equation. Corollary to the Polygon Interior Angles Theorem Combine like terms. Subtract 288 from each side. SOLUTION Example 4 Finding Angle Measures in Polygons a. The polygon is not equilateral or equiangular. So, the polygon is not regular. Polygon Interior Angles Theorem Write an equation. Combine like terms. Solve for x. SOLUTION b. Find the sum of the measures of the interior angles. Example 5 Finding an Unknown Exterior Angle Measure Find the value of x in the diagram. Use the Polygon Exterior Angles Theorem to write and solve an equation. Polygon Exterior Angles Theorem Combine like terms. Solve for x. SOLUTION Example 6 Finding Angle Measures in Regular Polygons The trampoline is shaped like a regular dodecagon. Find the measure of each (a) interior angle and (b) exterior angle. a. Use the Polygon Interior Angles Theorem to find the sum of the measures of the interior angles. SOLUTION b.
