Math Polygons Quiz Review Key

Name: Key Polygon Worksheet Honors Geometry Hour: Show all work. If you need a separate sheet of paper, attach it to this worksheet. 1. Name the polygon whose interior angles equal its exterior angles. Quadrilateral 2. How many sides does a polygon have if the sum of its interior angles is half the sum of its exterior angles? 180(n-2)=1/2(360) 180(n-2)=180 n-2=1 n=3 3. Two exterior angles of a pentagon 200°. Of the remaining three angles, the second angle is 20° less than twice the first angle. The third angle is 20° more than the first angle. Find the size of each angle.. E+1÷2=200 ∠1=x ∠2=2x-20 63=x+20 x+2x-20+x+20+160=540 x=95 95;170;115⁷ 4. Find the sum of the measures of the angles in an octagon. 180(8-2)=180*6=1080° 5. Find the number of diagonals that can be drawn in a pentadecagon. 15 sides 5-10 d=15(15-3)/2 90 6. If the measure of one of the angles of a regular polygon is 175°, find number of sides of the polygon. Ex+5° 360/5=72sides) For #7-15, give the most descriptive name for each polygon. 7. The sum of the measures of its angles is 1800°, Dodecagon Regular Decagon 13-gon 8. Each interior angle is 144°. 9. It has 65 diagonals. No guess and check. n²-3n=130 Regular Octagon n²-3n-130=0 (n-13)(n+10) 10. The measure of each interior angle is three times the measure of each exterior angle. 11. The sum of the angles is 1440°. 180(n-2)/n=3*360/n 45n=180n²-360n 0=180n²-1440n, Decagon 0=n(15n-1440) (n-11)(n+8) Reg. Nonagon 11-gon 12. Each interior angle is 140°, 13. It has 44 diagonals. No guess and check n²-3n=88 n²-3n-88>0 11, 14. The ratio of each interior angle to each exterior angle is 3:2 Reg. Pentagon 15. Each interior angle is congruent to each exterior angle. Reg. Quadrilateral Ex. + Int=180 (SQUARE) =90 6x=72 360/72=5 16. Find the measure of each angle in a regular decagon. \[144^{\circ}\] 17. How many sides does a polygon have if the sum of its interior angles is 2700°? 17 sides 18. The pentagon below is regular. Find x. \[X=72^{\circ}\] \[\frac{540}{5}=108\] \[108-36=\underline{72}\] 108 108, Final Day Review Problems: 1. Find the sum of the angles of a nonagon. \(n=9 S_{I}=180(n-2)\) \[150(9-2)=180.7=\boxed{1260^{\circ}}\] 2. A regular angle of \(168^{\circ}.\) How many \[6xt=180-168=\underline{12^{\circ}}\] E=360 n=300 \[n=\frac{260}{12}=\boxed{305idcs}\] 3. If a polygon how sides does it \[d=\frac{n(n-3)}{2}\] \[14=\frac{n^{2}-3a}{2}\] \[7n^{2}-3n=28\rightarrow n^{2}-3n-28=0\] 4. The sum of the angles polygon °. angle, n=7) \[3969=180(n-2)\rightarrow22=n-7\] L \[(n=24)\] \[(\underline{n}-7)(n+4)\] \[36\frac{0}{2}y=(E=15^{\circ})\] 5. What is the regular one of the shortest diagonals? 35 diags \[\frac{10}{35}=(\frac{2}{7})\] 6. Given ABCDEF is a regular hexagon \[DB=AE]\] Why? Find the \(m\angle BAE\) \[S_{1}=720\] \[\triangle BCD\cong\triangle AFE_{M}SAS\] 50 DB-AE by CPCTC C Each IntL-120 \[120-30=90^{\circ}\] \[\angle bAE=90^{\circ}\] \[B=120\] F E 7. Find \(m\angle1, m\angle2, m\angle3, m\angle4,\) and \(m\angle5.\) All polygons are \[m\angle1=\underline{60}m\angle2=\underline{120}m\angle3\underline{106}\] \[m\angle4=72^{\circ}m\angle5=\underline{132^{\circ}}\] 360-(120мов) \[12^{\circ}\] 360-120-108 132 120/60