Geometry Worksheet 6.1 and 6.2

Name: Keg Geometry Wkst 6.1 and 6.2 1) Two angles of a convex heptagon are congruent. Each of the other five angles has a measure twice that of the other two angles. Find the measure of each angle. 12x960 675 75, 75, 150, 150, 150, 150, 150 2) Your friend is working on a problem and claims that the sum of the measures of the interior angles of a convex polygon is 2070. Explain why this is not possible. 154175U 3) The sum of the measures of the interior angles of a regular polygon is 24,840. Write and solve an equation to find the number of sides the polygon has. langle n + 2Y(26) = 0.2454 1600=2530 11140 Sides 4) The sum of the measures of eight interior angles of a convex nonagon is 1190. Find the measure of the ninth angle. 1200-119010 5) The measure of an exterior angle of a regular polygon is 2x, and the measure of an interior angle is 4x. Find the number of sides in the polygon. 2x + 4x = 150 Sooxt=00 6x = 180 x = 30 766/66 Lo sides 6) The sum of the measures of the interior angles of a convex polygon is between 7300 and 7500, a. How many sides does the polygon have? (45 Rof Sules Suth of oil b. What is the exact sum of the measures of the interior angles? 730 40 93 45 45 7300 7982 17500 7740 7) Using a regular hexagon, extend each side to make a six-pointed star. Are the angles at the points of the star congruent? If so, what is the measure of each angle? Ps, 60 8) The measure of the exterior angles of a convex quadrilateral are x, 2x, 3x, and 4x. Find the value of x and the measure of each exterior angle. 10x = 360 y = 3 * k deg 36, 72, 108, 144 Extra Practice 6.1 Name Key In 1-8, decide whether the figure is a polygon. If It is not, explain why not. If it is, state whether it is convex. 1. 2. 3. NO PYS, CUNGC Cuced Yo 4. N Curved 5. 6. 7. re's Covere 'Convex 8. Yes conce In 9-14, use the polygon MNOPQRST. 9. What name is given to this polygon based upon the number of sides it has? Defen 10. Give two alternate names for polygon MNOPQRST. MTSRGPON 11. Name the consecutive sides to ORAS Nu M T N 12. Name the consecutive angles to N.20+ 13. Name the nonconsecutive angles to ZN. T, S, R, 14. Name the diagonals that contain vertex S. SH SN, 50, SP, S P 0 15. Which of the following polygons are equilateral? Which are equiangular? Which are regular? Which are hexagons? a. b. regular S R In 16-20, draw the figure and mark any congruent sides or angles. 16. A regular pentagon. 18. A nonconvex quadrilateral. 20. A regular octagon. See 21. Trace the five points and connect them with five line segments to form a polygon. Repeat the procedure to find as many different polygons as you can. Then name your pentagons. 17. A convex hexagon. 19. An equilateral quadrilateral that is not equangular. C 0 hexcy 10/ Geometry: Sec 6.2 wkot #1 Name 1) Det. the sum of the measures of the angles of a convex octagon. i(lm) =1080^ - 2) Det. the sum of the measures of the ext. angles of a convex nonagon. 360 3) Each of the first 5 angles of a convex hexagon has a measure of 130 deg What is the measure of the sixth angle? 5(130) + x = 10 x = 70xi 6.5 + x = 7.2 4) What is the measure of one ext. angle of a regular convex polygon of 16 sides? (36G)/(ik) = 0.5 5) How many sides regular convex polygon have if one int. angle is 156 deg ? ( T 1-2Y150) 11 =156 iN*mu*m = 16D*mu_{1} - 3mu*C 36033 n = 15 Sines 6) Each ext. angle of a regular convex polygon is 30 ^ 6 What is the sum of its int angles? n ni t * 2 plus/minus m * ir * 4 101800 7) How many diagonals can be drawn from 1 vertex regular convex polygon whose int. angles have a total of 2340 deg (n - 2)(115) = 2340 I_{3}*L_{11} = gamma / K_{11} 0=15 sars 15-3-12cdieques 8) Prove if convex: a) 9)The sum of the measures of the int. angles of a polygon is four times the sum of the measures of its ext. angles, one at each vertex. How many sides does the polygon have ? (n - a)(nw) = 4(bw) D = Ls * dx ) 10) in quad ABCD, A = X deg fB = 2 * x deg gamma*C = 3 * x deg and chi ^ gamma * D = 4x ^ 0 Find the value of x and then det. which of be t_{x} = ∞ * 0 II. (Sometimes, Always, or Never true?) D hhl 11) The sum of the measures of the ext. angles of any polygon, one angle at each vertex, is Calways 360" 12) A seg. joining two vertices of a polygon is a diagonal. (cealer) 13) A regular polygon is equilateral.