Find The Sum Of The Measures Of The Interior Angles Of .
Mid-Chapter Quiz: Lessons 6-1 through 6-3Find the sum of the measures of the interior angles of each convex polygon.1. pentagonSOLUTION:A pentagon has five sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior anglemeasures.Substitute n 5 in.2. heptagonSOLUTION:A heptagon has seven sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior anglemeasures.Substitute n 7 in.3. 18-gonSOLUTION:An 18-gon has eighteen sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior anglemeasures.Substitute n 18 in4. 23-gonSOLUTION:A 23-gon has twenty-three sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior anglemeasures.Substitute n 23 inFind the measure of each interior angle.5.SOLUTION:eSolutionsby CogneroThe Manualsum of- Poweredthe interiorangle measures isor 360.Page 1
Substitute n 23 in.Mid-Chapter Quiz: Lessons 6-1 through 6-3Find the measure of each interior angle.5.SOLUTION:The sum of the interior angle measures isor 360.Use the value of x to find the measure of each angle.6.SOLUTION:The sum of the interior angle measures isor 360.Use the value of x to find the measure of each angle.eSolutions Manual - Powered by CogneroPage 2
Mid-Chapter Quiz: Lessons 6-1 through 6-36.SOLUTION:The sum of the interior angle measures isor 360.Use the value of x to find the measure of each angle.The sum of the measures of the interior angles of a regular polygon is given. Find the number of sides inthe polygon.7. 720SOLUTION:Let n the number of sides in the polygon. By the Polygon Interior Angles Sum Theorem, the sum of the interior.angle measures can also be expressed as8. 1260SOLUTION:Let n the number of sides in the polygon. By the Polygon Interior Angles Sum Theorem, the sum of the interiorangle measures can also be expressed as.eSolutions Manual - Powered by Cognero9. 1800SOLUTION:Page 3
Mid-Chapter Quiz: Lessons 6-1 through 6-38. 1260SOLUTION:Let n the number of sides in the polygon. By the Polygon Interior Angles Sum Theorem, the sum of the interiorangle measures can also be expressed as.9. 1800SOLUTION:Let n the number of sides in the polygon. By the Polygon Interior Angles Sum Theorem, the sum of the interiorangle measures can also be expressed as.10. 4500SOLUTION:Let n the number of sides in the polygon. By the Polygon Interior Angles Sum Theorem, the sum of the interiorangle measures can also be expressed as.Find the value of x in each diagram.11.SOLUTION:Use the Polygon Exterior Angles Sum Theorem to write an equation. Then solve for x.eSolutions Manual - Powered by CogneroPage 4
Mid-Chapter Quiz: Lessons 6-1 through 6-312.SOLUTION:Use the Polygon Exterior Angles Sum Theorem to write an equation. Then solve for x.UseWXYZ to find each measure.13.SOLUTION:We know that consecutive angles in a parallelogram are supplementary.So,Solve for.14. WZSOLUTION:We know that opposite sides of a parallelogram are congruent.So, WZ XY 24.15.SOLUTION:We know that opposite angles of a parallelogram are congruent.So,16. DESIGN Describe two ways to ensure that the pieces of the design shown would fit properly together.eSolutions Manual - Powered by CogneroPage 5SOLUTION:The pieces of the design would fit properly together if the opposite sides are congruent or if the opposite angles are
15.SOLUTION:We know thatoppositeanglesa parallelogramare congruent.Mid-ChapterQuiz:Lessons6-1 ofthrough6-3So,16. DESIGN Describe two ways to ensure that the pieces of the design shown would fit properly together.SOLUTION:The pieces of the design would fit properly together if the opposite sides are congruent or if the opposite angles arecongruent. Sample answer: Make sure that opposite sides are congruent or make sure that opposite angles arecongruent.ALGEBRA Find the value of each variable.17.SOLUTION:We know that diagonals of a parallelogram bisect each other.So, s – 7 6 and 2t – 6 8.Solve for s and b.So, s 13 and t 7.18.SOLUTION:We know that opposite sides of a parallelogram are congruent.3f – 6 2f 8f 14We know that consecutive angles in a parallelogram are supplementary.So,Solve for d.19. PROOF Write a two-column proof.Given:Prove:eSolutions Manual - Powered by CogneroPage 6
Solve for d.Mid-Chapter Quiz: Lessons 6-1 through 6-319. PROOF Write a two-column proof.Given:Prove:SOLUTION:You need to walk through the proof step by step. Look over what you are given and what you need to prove. Here,you are given. You need to prove. Use the properties that you have learned aboutparallelograms to walk through the proof.Proof:Statements (Reasons)1.(Given)2.(Opp.3.(Transitive Prop.))Find x and y so that each quadrilateral is a parallelogram.20.SOLUTION:We know that opposite sides of a parallelogram are congruent.2x 2 x 5x 3Similarly, 2y 5 y 10.So, y 5.21.SOLUTION:We know that opposite sides of a parallelogram are congruent.3x – 2 2x 6x 8Similarly, 6y – 8 4y 6.So, y 7.22. MUSIC Why will the keyboard stand shown below always remain parallel to the floor?eSolutions Manual - Powered by CogneroPage 7
We know that opposite sides of a parallelogram are congruent.3x – 2 2x 6x 8Similarly, 6yQuiz:4y 6. 6-1 through 6-3Mid-Chapter– 8 LessonsSo, y 7.22. MUSIC Why will the keyboard stand shown below always remain parallel to the floor?SOLUTION:Let the top of the stand represent one side of the quadrilateral and let the bottom of the stand represent the oppositeside of the same quadrilateral. The legs can now represent the diagonals of the quadrilateral. Since the legs arejoined at their midpoints, the legs bisect each other. If the diagonals of a quadrilateral bisect each other, than thequadrilateral is a parallelogram. The opposite sides of a parallelogram are always parallel. Therefore, the keyboardwill always be parallel to the floor.23. MULTIPLE CHOICE Which of the following quadrilaterals is not a parallelogram?ABCDSOLUTION:Test choice A. This quadrilateral has one pair of opposite sides both parallel and congruent. This is sufficient toprove that this quadrilateral is a parallelogram.Test choice B. This quadrilateral has both pairs of opposite sides congruent. This is sufficient to prove that thisquadrilateral is a parallelogram.Test choice C. This quadrilateral has diagonals that bisect each other. This is sufficient to prove that this quadrilateralis a parallelogram.Test choice D. This quadrilateral has one pair of opposite sides parallel. That is not sufficient proof that thisquadrilateral is a parallelogram.The correct answer is D.COORDINATE GEOMETRY Determine whether the figureis a parallelogram. Justify your answer with themethod indicated.24. A(–6, –5), B(–1, –4), C(0, –1), D(–5, –2); Distance FormulaeSolutions Manual - Powered by CogneroSOLUTION:Use the Distance Formula to find the distance.Page 8
Test choice C. This quadrilateral has diagonals that bisect each other. This is sufficient to prove that this quadrilateralis a parallelogram.Test choice D. This quadrilateral has one pair of opposite sides parallel. That is not sufficient proof that thisquadrilateralis a parallelogram.Mid-ChapterQuiz:Lessons 6-1 through 6-3The correct answer is D.COORDINATE GEOMETRY Determine whether the figureis a parallelogram. Justify your answer with themethod indicated.24. A(–6, –5), B(–1, –4), C(0, –1), D(–5, –2); Distance FormulaSOLUTION:Use the Distance Formula to find the distance.So, the distance between A and B is.So, the distance between B and C is.Therefore, the distance between C and D isThe distance between D and A is. Since both pairs of opposite sides are congruent, ABCD is a parallelogram.25. Q(–5, 2), R(–3,–6), S(2, 2), T(–1, 6); Slope FormulaSOLUTION:Use the slope formula.eSolutions Manual - Powered by CogneroSince the slope ofslope ofPage 9, QRST is not a parallelogram.
Mid-ChapterQuiz:Lessons6-1A through6-3 both pairs of opposite sides are congruent, ABCD is a parallelogram.The distancebetweenD andis. Since25. Q(–5, 2), R(–3,–6), S(2, 2), T(–1, 6); Slope FormulaSOLUTION:Use the slope formula.Since the slope ofslope ofeSolutions Manual - Powered by Cognero, QRST is not a parallelogram.Page 10
Sep 27, 2014 · By the Polygon Interior Angles Sum Theorem, the sum of the interior angle measures can also be expressed as . Find the value of x in each diagram. 62/87,21 Use the Polygon Exterior Angles Sum Theorem to write an equation. Then solve for x. 62/87,21 Use the Polygon Exterior Angles
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Le genou de Lucy. Odile Jacob. 1999. Coppens Y. Pré-textes. L’homme préhistorique en morceaux. Eds Odile Jacob. 2011. Costentin J., Delaveau P. Café, thé, chocolat, les bons effets sur le cerveau et pour le corps. Editions Odile Jacob. 2010. 3 Crawford M., Marsh D. The driving force : food in human evolution and the future.
