Geometry Section Finding Angle Measures in Polygons

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Find Angle Measures in Polygons

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Find Angle Measure in Polygons

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Presentation transcript:

Geometry Section 8.1 - Finding Angle Measures in Polygons I can find the sum of the interior angles of a given convex polygon I can find the measure of the missing interior or exterior angle in a convex polygon.

What is the sum of the interior angles of the following polygon?

1 4 2 _+_+_=180

Find the sum of angle measures in a polygon EXAMPLE 1 Find the sum of angle measures in a polygon Find the sum of the measures of the interior angles of a convex octagon. SOLUTION An octagon has 8 sides. Use the Polygon Interior Angles Theorem. (n – 2) 180° = (8 – 2) 180° Substitute 8 for n. = 6 180° Subtract. = 1080° Multiply. ANSWER The sum of the measures of the interior angles of an octagon is 1080°.

Find the number of sides of a polygon EXAMPLE 2 Find the number of sides of a polygon The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the number of sides. SOLUTION 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. (n –2) 180° = 900° Polygon Interior Angles Theorem n –2 = 5 Divide each side by 180°. n = 7 Add 2 to each side. The polygon has 7 sides. It is a heptagon. ANSWER

EXAMPLE 3 Find an unknown interior angle measure ALGEBRA Find the value of x in the diagram shown. The value of x is 72. ANSWER

Walking the Polygon Activity Walker – This person will walk the perimeter of the polygon Spinner – This person stays in place but always faces the same direction the walker is facing. Observers – These people are responsible for making sure that the walker and the spinner are following directions and observing the directions the turner faces as the walker walks the perimeter of the polygon.

Standardized Test Practice EXAMPLE 4 Standardized Test Practice SOLUTION] Use the Polygon Exterior Angles Theorem to write and solve an equation. x° + 2x° + 89° + 67° = 360° Polygon Exterior Angles Theorem 3x + 156 = 360 Combine like terms. x = 68 Solve for x. The correct answer is B. ANSWER

EXAMPLE 5 Find angle measures in regular polygons TRAMPOLINE The trampoline shown is shaped like a regular dodecagon. Find (a) the measure of each interior angle and (b) the measure of each exterior angle.