Interior Angles of a Polygon Worksheet PDF<\/h2>\n
Example 1. i)In the first diagram, no. of sides is 7. Example 2.<\/strong> The number of sides of a heptagon is 7. Example 3.<\/strong> Given that, Example 4.<\/strong> Given that, Example 5.<\/strong> Given that, Example 6.<\/strong> Given that, each interior angle = 120\u00b0 Example 7.<\/strong> Given that, Example 8.<\/strong> Given that the angle of a hexagon is (x \u2013 5)\u00b0, (x \u2013 8)\u00b0, (2x \u2013 9)\u00b0,\u00a0 x, (2x \u2013 6)\u00b0, and (x \u2013 4)\u00b0. Example 9.<\/strong> Given that the angles of a heptagon are in the ratio 1: 2 : 3: 4: 5: 6: 8. Example 10.<\/strong> Given that, Example 11.<\/strong> Given that, Example 12.<\/strong> Given that, \u00a0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Try our Worksheet on Interior Angles of a Polygon to solve a variety of problems such as finding the sum of interior angles of a polygon, finding the missing angle in a polygon, etc.\u00a0 These engaging activities in Interior Angles of a Polygon Worksheet PDFs with regular and irregular polygons are all you need to … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143315"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=143315"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143315\/revisions"}],"predecessor-version":[{"id":143316,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143315\/revisions\/143316"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=143315"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=143315"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=143315"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n<\/strong>Find the sum of interior angles of each polygon
\n![\"polygon](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/polygon-example1.jpg\")
![\"polygon](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/polygon-example1-diagram2.jpg\")
![\"polygon](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/polygon-example1-diagram3.jpg\")
<\/p>\nSolution:<\/strong><\/summary>\n
\nwe know that Sum of interior angles of a polygon is (n-2) \u00d7 180.
\nHere n=7
\n=(7-2) \u00d7 180
\n=5 \u00d7 180
\n=9000<\/sup>
\nTherefore, Sum of interior angles of a polygon is 9000<\/sup>.
\nii) In the second diagram, no. of sides is
\nAs we know that Sum of interior angles of a polygon is (n-2) \u00d7 180.
\nHere n=4
\n=(4-2)\u00d7 180
\n=2 \u00d7 180
\n=3600<\/sup>
\nTherefore, Sum of interior angles of a polygon is 3600<\/sup>.
\niii) In the third diagram, no. of sides is 5.
\nwe know that Sum of interior angles of a polygon is (n-2) \u00d7 180.
\nHere n=5
\n=(5-2)\u00d7 180
\n=3\u00d7 180
\n=540
\nTherefore, Sum of interior angles of a polygon is 5400<\/sup>.<\/p>\n<\/details>\n
\n
\nFind the interior angles of a regular heptagon and a regular octagon.
\n![\"heptagon](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/heptagon-example2-150x150.jpg\")
\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ![\"regular](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/regular-octagon-example2.jpg\")
<\/p>\nSolution:<\/strong><\/summary>\n
\nThe formula for finding the interior angles of a heptagon is, ((n-2)180\u00b0)\/n.
\nHere, ‘n’ or the number of sides is 7.
\nInterior angles of a heptagon = ((7-2)180\u00b0)\/8.
\n=5 \u00d7180\u00b0\/8
\n= 900\/8
\n=112.5\u00b0
\nTherefore, the interior angles of a regular heptagon = 112.5\u00b0 each.
\nThe number of sides of an octagon is 8.
\nThe formula for finding the interior angles of a polygon is, ((n-2)180\u00b0)\/n.
\nHere, ‘n’ or the number of sides is 8.
\nInterior angles of a octagon = ((8-2)180\u00b0)\/8.
\n= 6\u00d7180\u00b0\/8
\n= 1080\/8
\n= 135\u00b0
\nTherefore, the interior angles of a regular octagon = 135\u00b0 each.<\/p>\n<\/details>\n
\n
\nThe four interior angles of a pentagon are 1050<\/sup>,1180<\/sup>,750<\/sup>,1300<\/sup>. Find the other angle?
\n![\"pentagon](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/pentagon-example3.jpg\")
<\/p>\nSolution:<\/strong><\/summary>\n
\nThe four interior angles of a pentagon are 1050<\/sup>,1180<\/sup>,750<\/sup>,1300<\/sup>.
\nWe know that sum of angles of the pentagon is 540.
\nLet the other angle be x.
\n105+118+75+130+x=540
\n428+x=540
\nx=540-428
\n=112
\nTherefore, the other angle of a polygon is 1120<\/sup>.<\/p>\n<\/details>\n
\n
\nFind the number of sides in a polygon if the sum of its interior angles is 10800<\/sup>.<\/p>\nSolution:<\/strong><\/summary>\n
\nThe sum of its interior angles is 10800
\n<\/sup>Let no. of sides =n
\nSum of angles of polygon =1080
\n(n\u22122)\u00d7180=1080
\nn\u22122=1080\/180
\n\u200bn\u22122=6
\nn=6+2
\nn=8
\nTherefore, no. of sides of the polygon is 8.<\/p>\n<\/details>\n
\n
\nThe interior angle of a polygon is 60 degrees. The other interior angles are all equal to 120 degrees. How many sides does a\u00a0 polygon have?<\/p>\nSolution:<\/strong><\/summary>\n
\nThe interior angle of a polygon is 60 degrees
\n<\/strong>The other interior angles are all equal to 110 degrees.
\nLet the number of sides be x.
\nThere are x-1 no. of angles,120 degrees.
\nwe know that total interior angles of a polygon=180(sides-2)
\n180(x-2)=60+120(x-1)
\n180x-360=60+120x-120
\n180x-360=-60+120x
\n60x=-60+360
\n60x=300
\nx=300\/60=5
\nTherefore, the polygon has 5 sides.<\/p>\n<\/details>\n
\n
\nIf each interior angle is equal to 120\u00b0, then how many sides does a regular polygon have?<\/p>\nSolution:<\/strong><\/summary>\n
\nWe know that, Interior angle + Exterior angle = 180\u00b0
\nExterior angle = 180\u00b0-120\u00b0
\nTherefore, the exterior angle is 60\u00b0
\nThe formula for finding the number of sides of a regular polygon is =360\u00b0 \/ Magnitude of each exterior angle
\nTherefore, the number of sides = 360\u00b0 \/ 60\u00b0 = 6 sides
\nHence, the polygon has 6 sides.<\/p>\n<\/details>\n
\n
\nThe three angles of a polygon are 120\u00b0, 100\u00b0, 140\u00b0, and the other two angles are equal. Find the measure of these equal angles?<\/p>\nSolution:<\/strong><\/summary>\n
\nThe three angles of a polygon are 120\u00b0, 100\u00b0, 140\u00b0.
\nHere the polygon has six angles. Therefore, it is a hexagon.
\nThe sum of interior angles of a polygon=(n-2)180,n is no. of sides
\n=(6-2)\u00d7180
\n=4\u00d7180
\n=720
\nLet x be the measure of three angles that have the same measure.
\n3x+120+100+140=720
\n3x+360=720
\n3x=720-360
\n3x=360
\nx=360\/3=1200<\/sup>
\nTherefore, the three angles with the same measure have a measurement of 1200<\/sup>.<\/p>\n<\/details>\n
\n
\nThe angles of a hexagon are (x \u2013 5)\u00b0, (x \u2013 8)\u00b0, (2x \u2013 9)\u00b0,\u00a0 x,(2x-6)0,<\/sup> and (x \u2013 4)\u00b0. Find the value of x and the measure of all angles.<\/p>\nSolution:<\/strong><\/summary>\n
\nWe know that sum of angles of a hexagon is 7200<\/sup>.
\nTherefore, (x \u2013 5)\u00b0+ (x \u2013 8)\u00b0+ (2x \u2013 9)\u00b0+ (2x \u2013 6)\u00b0+ x+ (x \u2013 4)\u00b0=7200<\/sup>
\n8x-32=7200<\/sup>
\n8x=752
\nx=752\/8=940<\/sup>
\nTherefore, x=940<\/sup>
\nx-5=94-5=890<\/sup>
\nx-8=94-8=860<\/sup>
\n2x-9=2(94)-9=1790<\/sup>
\n2x-6=2(94)-6=1820<\/sup>
\nx-4=94-4=900<\/sup>.
\nHence, the angles of a hexagon are 940<\/sup>,890<\/sup>,860<\/sup>,1790<\/sup>,1820<\/sup>,900<\/sup>.<\/p>\n<\/details>\n
\n
\nThe angle of a heptagon is in the ratio 1: 2 : 3: 4: 5: 6: 8. Find the measure of the smallest and the biggest angles.<\/p>\nSolution:<\/strong><\/summary>\n
\nLet each angle be of x then,
\n1=x,
\n2=2x
\n3=3x
\n4=4x
\n5=5x
\n6=6x
\n8=8x
\nWe know that sum of angles of the heptagon is 9000<\/sup>.
\n1x+2x+3x+4x+5x+6x+8x=9000<\/sup>
\n29x=9000<\/sup>
\nx=9000<\/sup>\/29=310<\/sup>
\nHere the smallest angle is x=310<\/sup>.
\nThe largest angle is 8x=8(31)=2480<\/sup>.
\nTherefore, the smallest angle and the largest angle are 310<\/sup>,2470<\/sup>.<\/p>\n<\/details>\n
\n
\nThe four angles of the pentagon are equal and the fifth angle measure 120\u00b0. Find the measure of four equal angles?<\/p>\nSolution:<\/strong><\/summary>\n
\nThe four angles of the pentagon are equal.
\nThe fifth angle measure= 120\u00b0
\nLet x be the measure of four angles that have the same measure.
\nWe know that the sum of the angles of the pentagon is 3600<\/sup>.
\n4x+120=3600<\/sup>
\n4x=360-120
\n4x=240
\nx=240\/4=600<\/sup>.
\nTherefore, the measure of four equal angles is 600<\/sup>.<\/p>\n<\/details>\n
\n
\nThe seven angles of an octagon are 120\u00b0 each. Find the measure of the eighth angle?<\/p>\nSolution:<\/strong><\/summary>\n
\nThe seven angles of an octagon are 120\u00b0 each.
\nAn octagon has 8 sides.
\nThe Sum of angles of an octagon is (n-2)180=(8-2)180
\n=6(180)
\n=1080
\nLet the other angle be x.
\nx+7(120)=1080
\nx+840=1080
\nx=1080-840
\nx=240
\nHence, the measure of eight angles is 240\u00b0.<\/p>\n<\/details>\n
\n
\nIf the ratio of the number of sides of two regular polygons is 4:5 and the ratio of the sum of their interior angles is 11:14. Find the number of sides in both the polygons?<\/p>\nSolution:<\/strong><\/summary>\n
\nThe ratio of the number of sides of two regular polygons = 4:5
\nLet them be 4X and 5X
\nThe number of sides in the first polygon = 4X
\nThe number of sides in the second polygon = 5X
\nWe know that
\nThe sum of the interior angles in a regular polygon of n sides is (n-2)\u00d7180\u00b0
\nThe sum of the interior angles in the first polygon of 4X sides = (4X-2)\u00d7180\u00b0
\nThe sum of the interior angles in the second polygon of 5X sides = (5X-2)\u00d7180\u00b0
\nThe ratio of the sum of the interior angles of the two polygons = [(4X-2)\u00d7180\u00b0]:[(5X-2)\u00d7180\u00b0]
\n(4X-2) : (5X-2)
\nAccording to the given problem
\nThe ratio of the sum of their interior angles = 11:14
\n=> (4X-2) : (5X-2) = 11:14
\n=> (4X-2) \/ (5X-2) = 11 \/ 14
\nOn applying cross multiplication then
\n=>14(4X-2) = 11(5X-2)
\n=> 56X – 28 = 55X – 22
\n=> 56X – 55X = 28- 22
\n=> X = 6
\nSo,
\nThe number of sides in the first polygon
\n= 4(6) = 24.
\nThe number of sides in the second polygon= 5(6) = 30.
\nHence, the number of sides of polygons is 24 and 30.<\/p>\n<\/details>\n
\n