Do Now Take out your 5.1 worksheet and put it on your desk ready to be stamped. Take out a protractor and a calculator. How many degrees are in a 32-gon?

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Presentation transcript:

Do Now Take out your 5.1 worksheet and put it on your desk ready to be stamped. Take out a protractor and a calculator. How many degrees are in a 32-gon? How many degrees are in each angle of a regular pentagon? Find the missing angle to the right.

Exit Slip Error Analysis Compare your exit slip to Sarahy’s.

Polygon Exterior Angles

Today’s Objectives Discover the sum of the measures of the exterior angles of a polygon. Write formulas for the measure of the interior angle of an equiangular polygon. Use problem solving skills

Exterior angles The angle between any side of a shape, and a line extended from the next side Forms a linear pair with an interior angle

Investigation: Exterior Angle Sum Draw a large polygon. Extend its sides to form a set of exterior angles. Measure all the interior angles of the polygon except one. Use the Polygon Sum Conjecture to calculate the measure of the last interior angle. Check your answer with a protractor. Use the Linear Pair Conjecture to calculate the measure of each exterior angle. Calculate the sum of the measures of the exterior angles. # of sides of polygon 3 4 5 6 7 8 … n Sum of measures of exterior angles

Exterior Angle Sum Conjecture For any polygon, the sum of the measures of a set of exterior angles is ____. 360o.

Geogebra Example How does this demonstrate the Exterior Angle Sum Theorem? The exterior angles slide into place as angles around a point, which always add up to 360o. Using the Polygon Sum Conjecture, write a formula for the measure of each interior angle in an equiangular polygon. 180o(n—2) . n Using the Exterior Angle Sum Conjecture, write the formula for the measure of each exterior angle in an equiangular polygon. 360o

Practice How many degrees are in each exterior angle?

Challenge Is there another way to find an interior angle measure of an equiangular polygon? Hint: What if you know the measure of each exterior angle?

Equiangular Polygon Conjecture You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: 180o(n—2) . n 180 — 360o

Practice What is the sum of the measures of the exterior angles of a decagon? What is the measure of one exterior angle of an equiangular pentagon?

Review

Review

Review

Practice

Exit Slip What is the sum of the measures of the exterior angles of a nonagon? What is the measure of one exterior angle of an equiangular hexagon? Find a. Show your work and explain your reasoning.

Honors Exit Slip What is the sum of the measures of the exterior angles of a nonagon? What is the measure of one exterior angle of an equiangular hexagon? Find a and b. Show your work and explain your reasoning.