What is the measure of one of the interior angle of a regular dodecagon? <\/p>\n\n\n\n
A. 150\u00b0 <\/p>\n\n\n\n
B. 135\u00b0 <\/p>\n\n\n\n
C. 108\u00b0 <\/p>\n\n\n\n
D. 144\u00b0<\/p>\n\n\n\n
The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n The correct answer is D. 144\u00b0<\/strong>.<\/p>\n\n\n\n To calculate the measure of one of the interior angles of a regular dodecagon (12-sided polygon), we can use the formula for the interior angle of a regular polygon: Interior angle=(n\u22122)\u00d7180\u00b0n\\text{Interior angle} = \\frac{(n – 2) \\times 180\u00b0}{n}<\/p>\n\n\n\n where nn is the number of sides of the polygon. In this case, a dodecagon has n=12n = 12 sides. Substituting this value into the formula: Interior angle=(12\u22122)\u00d7180\u00b012\\text{Interior angle} = \\frac{(12 – 2) \\times 180\u00b0}{12} Interior angle=10\u00d7180\u00b012\\text{Interior angle} = \\frac{10 \\times 180\u00b0}{12} Interior angle=1800\u00b012\\text{Interior angle} = \\frac{1800\u00b0}{12} Interior angle=150\u00b0\\text{Interior angle} = 150\u00b0<\/p>\n\n\n\n So, the interior angle of a regular dodecagon is 150\u00b0<\/strong>.<\/p>\n\n\n\n If the question were asking for the exterior angle, we would use the formula: Exterior angle=360\u00b0n\\text{Exterior angle} = \\frac{360\u00b0}{n}<\/p>\n\n\n\n For a dodecagon, this would be: Exterior angle=360\u00b012=30\u00b0\\text{Exterior angle} = \\frac{360\u00b0}{12} = 30\u00b0<\/p>\n\n\n\n Finally, the interior angle and the exterior angle of a regular polygon are supplementary, meaning they add up to 180\u00b0. So, for a dodecagon: Interior angle+Exterior angle=180\u00b0\\text{Interior angle} + \\text{Exterior angle} = 180\u00b0 150\u00b0+30\u00b0=180\u00b0150\u00b0 + 30\u00b0 = 180\u00b0<\/p>\n\n\n\n Therefore, 150\u00b0<\/strong> is the correct measure of one of the interior angles.<\/p>\n","protected":false},"excerpt":{"rendered":" What is the measure of one of the interior angle of a regular dodecagon? A. 150\u00b0 B. 135\u00b0 C. 108\u00b0 D. 144\u00b0 The correct answer and explanation is: The correct answer is D. 144\u00b0. To calculate the measure of one of the interior angles of a regular dodecagon (12-sided polygon), we can use the formula […]<\/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-44295","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44295","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=44295"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44295\/revisions"}],"predecessor-version":[{"id":44296,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/44295\/revisions\/44296"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=44295"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=44295"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=44295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}