{"id":36887,"date":"2025-06-25T10:06:31","date_gmt":"2025-06-25T10:06:31","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=36887"},"modified":"2025-06-25T10:06:32","modified_gmt":"2025-06-25T10:06:32","slug":"the-sum-of-seven-interior-angles-of-1000a","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-sum-of-seven-interior-angles-of-1000a\/","title":{"rendered":"The sum of seven interior angles of 1000\u00c2\u00b0."},"content":{"rendered":"\n<p>The sum of seven interior angles of 1000\u00c2\u00b0. Find the eighth angle. Octagon is? Please answer step by step fast, please. I have to complete my work for my school.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The sum of seven interior angles of an <strong>octagon<\/strong> is <strong>1000\u00b0<\/strong>.<\/li>\n\n\n\n<li>We are to find the <strong>eighth angle<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Step-by-step Solution:<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Step 1: Understand the problem<\/h4>\n\n\n\n<p>An <strong>octagon<\/strong> has <strong>8 sides<\/strong>, so it has <strong>8 interior angles<\/strong>.<br>We are given the sum of <strong>7 of these angles = 1000\u00b0<\/strong>, and we are to find the <strong>eighth<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Step 2: Use the formula for the sum of interior angles<\/h4>\n\n\n\n<p>For any polygon with <strong>n sides<\/strong>, the <strong>sum of interior angles<\/strong> is:Sum=(n\u22122)\u00d7180\u2218\\text{Sum} = (n &#8211; 2) \\times 180^\\circSum=(n\u22122)\u00d7180\u2218<\/p>\n\n\n\n<p>For an <strong>octagon<\/strong> (n = 8):Sum=(8\u22122)\u00d7180=6\u00d7180=1080\u2218\\text{Sum} = (8 &#8211; 2) \\times 180 = 6 \\times 180 = 1080^\\circSum=(8\u22122)\u00d7180=6\u00d7180=1080\u2218<\/p>\n\n\n\n<p>So, the total sum of <strong>all 8 interior angles<\/strong> of an octagon is <strong>1080\u00b0<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">Step 3: Subtract the sum of the 7 known angles<\/h4>\n\n\n\n<p>We are told that the <strong>sum of seven interior angles = 1000\u00b0<\/strong><\/p>\n\n\n\n<p>So, the <strong>eighth angle = 1080\u00b0 &#8211; 1000\u00b0 = 80\u00b0<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 Final Answer:<\/h3>\n\n\n\n<p>80\u2218\\boxed{80^\\circ}80\u2218\u200b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (No em dashes):<\/h3>\n\n\n\n<p>An octagon is a polygon with eight sides. Every polygon has a total interior angle sum that depends on the number of sides it has. The formula to find the total interior angle sum is to take the number of sides, subtract two, and multiply the result by 180 degrees. This rule comes from dividing the polygon into triangles. Each triangle contributes 180 degrees to the total angle sum.<\/p>\n\n\n\n<p>For an octagon, we apply the formula like this: (8 &#8211; 2) \u00d7 180 = 6 \u00d7 180 = 1080 degrees. This means that if we add up all eight interior angles of an octagon, we should get 1080 degrees.<\/p>\n\n\n\n<p>In this problem, we are told that seven of the interior angles already add up to 1000 degrees. Since the total for all eight is 1080 degrees, we can subtract the known sum of seven angles from the total. So, 1080 degrees minus 1000 degrees equals 80 degrees. This is the missing eighth angle.<\/p>\n\n\n\n<p>This approach is based purely on geometry and works for any polygon. You can always find a missing angle if you know the total interior angle sum and the values of the other angles. This method helps not only with octagons but also with other shapes like pentagons, hexagons, or decagons. It is important to understand and remember the basic formula for interior angle sums. Once you know that, solving problems like this becomes easy and fast.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-823.jpeg\" alt=\"\" class=\"wp-image-36896\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-823.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-823-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-823-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The sum of seven interior angles of 1000\u00c2\u00b0. Find the eighth angle. Octagon is? Please answer step by step fast, please. I have to complete my work for my school. The Correct Answer and Explanation is: We are given: \u2705 Step-by-step Solution: Step 1: Understand the problem An octagon has 8 sides, so it has [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-36887","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36887","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=36887"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36887\/revisions"}],"predecessor-version":[{"id":36897,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/36887\/revisions\/36897"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=36887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=36887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=36887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}