Find the value of x in each triangle

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Presentation transcript:

Find the value of x in each triangle. 1. 2. 1. 2. 3. Two angles of a triangle measure 35° and 65°. What is the measure of the third angle? 4. Two angles of a triangle measure 25° and 45°. What is the measure of the third angle? 5. The measures of the angles of a triangle are in the ratio 2:3:3. What are the measures of the angles? Course3, Lesson 5-4

ANSWERS 1. 90 2. 15 3. 100° 4. 110° 5. 45°; 67.5°; 67.5° Course3, Lesson 5-4

HOW can algebraic concepts be applied to geometry? Course3, Lesson 5-4

Mathematical Practices Geometry Extension of 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by transversal, and the angle-angle criterion for similarity of triangles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. Course3, Lesson 5-4 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

find the measure of an interior or exterior angle of a regular polygon Geometry To find the measure of an interior or exterior angle of a regular polygon Course3, Lesson 5-4.

polygon equiangular regular polygon Geometry polygon equiangular regular polygon Course3, Lesson 5-4

Interior Angle Sum of a Polygon Geometry Interior Angle Sum of a Polygon Words The sum of the measures of the interior angles of a polygon is (n – 2)180, where n represents the number of sides. Symbols S = (n – 2)180 Course3, Lesson 5-4

Find the sum of the measures of the interior angles of a decagon. Step-by-Step Example 1. Find the sum of the measures of the interior angles of a decagon. 1 S = (n – 2) 180 Write the equation. S = (10 – 2) 180 2 A decagon has 10 sides. Replace n with 10. 3 S = (8)180 or 1,440 Simplify. The sum of the measures of the interior angles of a decagon is 1,440°. 4 Need Another Example?

Find the sum of the measures of the interior angles of a 13-gon. Need Another Example? Find the sum of the measures of the interior angles of a 13-gon. 1,980° Answer

Find the sum of the measures of the angles. Step-by-Step Example 2. Each chamber of a bee honeycomb is a regular hexagon. Find the measure of an interior angle of a regular hexagon. 1 Find the sum of the measures of the angles. S = (n – 2) 180 Write an equation. S = (6 – 2) 180 Replace n with 6. S = (4)180 or 720 Simplify. 2 The sum of the measures of the interior angles is 720°. Divide 720 by 6, the number of interior angles, to find the measure of one interior angle. So, the measure of one interior angle of a regular hexagon is 720° ÷ 6 or 120°. 3 Need Another Example?

Need Another Example? A designer is creating a new logo for a bank. The logo consists of a regular pentagon surrounded by isosceles triangles. Find the measure of an interior angle of a regular pentagon. 108° Answer

Exterior Angles of a Polygon Geometry Exterior Angles of a Polygon Words In a polygon, the sum of the measures of the exterior angles, one at each vertex, is 360˚ Model Symbols Course3, Lesson 5-4

Find the measure of an exterior angle in a regular hexagon. Step-by-Step Example 3. Find the measure of an exterior angle in a regular hexagon. 1 Let x represent the measure of each exterior angle. 2 6x = 360 Write an equation. A hexagon has 6 exterior angles. 3 x = 60 Division Property of Equality 4 So, each exterior angle of a regular hexagon measures 60°. Need Another Example?

Find the measure of an exterior angle in a regular 30-gon. Need Another Example? Find the measure of an exterior angle in a regular 30-gon. 12° Answer

How did what you learned today help you answer the Geometry How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Course 3, Lesson 5-4

How did what you learned today help you answer the Geometry How did what you learned today help you answer the HOW can algebraic concepts be applied to geometry? Sample answers: You use a formula to find the sum of the interior angles of any polygon. You can write an equation to find the measure of a missing interior or exterior angle of a polygon. Course 3, Lesson 5-4

Geometry Functions Ratios and Proportional Relationships Explain how to find the sum of the interior angles of a polygon when you know the number of sides of the polygon. Course 3, Lesson 5-4