{"id":12280,"date":"2017-06-12T16:03:15","date_gmt":"2017-06-12T11:03:15","guid":{"rendered":"http:\/\/jworldtimes.com\/old-site\/jwt2015\/?p=12280"},"modified":"2019-11-19T10:51:27","modified_gmt":"2019-11-19T05:51:27","slug":"angles-triangles","status":"publish","type":"post","link":"https:\/\/www.jworldtimes.com\/old-site\/css-exclusive\/css-special\/angles-triangles\/","title":{"rendered":"Angles & Triangles"},"content":{"rendered":"

\"Angles<\/a><\/p>\n

Angle<\/strong><\/p>\n

An angle is a combination of \u201ctwo rays\u201d (half lines) with a common end point.
\na.<\/strong> Common end point = vertex
\nb.<\/strong> Rays as the sides = legs or arms of the angle.
\nAcute angle<\/strong>
\nLess than 90o
\na.<\/strong> An angle whose measure is less than 90o is called an acute angle.
\nb.<\/strong> Acute angles are the smallest being between 0 and 90o.
\nObtuse angle<\/strong>
\nBetween 90o and 180o
\nAn angle whose measure is greater than 90o but less than 180o, is called an obtuse angle.
\nRight angle<\/strong>
\nAn angle whose measure is exactly 90o.
\nStraight angle<\/strong>
\nAn angle whose measure is exactly 180o i.e. a straight line
\nReflex angle<\/strong>
\nAn angle whose measure is greater than 180 o but less than 360o is a reflex angle.
\nFull angle<\/strong>
\nAn angle whose measure is exactly 3600 i.e. a full circle
\nAllied angles<\/strong>
\na.<\/strong> \u201cAllied angle is an angle pair, which is created by trans-versal line.\u201d
\nb.<\/strong> Allied angles are also known as:
\n(i) Co-interior\u00a0\u00a0 \u00a0(ii) Adjacent interior
\nExplanation<\/strong>
\na.<\/strong> If I draw two parallel lines cut by a transversal, then allied angles are between the parallel lines and on the same side of transversal.
\nb.<\/strong> The allied angle theorem states that allied angles are supplementary.
\nc.<\/strong> A line that meets two or more parallel lines is called a transversal line.
\n5.<\/strong> Complementary angles<\/strong><\/p>\n

a.<\/strong> Two angles whose sum totals 90o degree.
\nb.<\/strong> Two angles are complementary when they add up to 90o degrees.
\nc.<\/strong> They don\u2019t have to be next to each other; just the sum total must be 90o.
\nExample<\/strong>
\n(i)<\/strong> 60o and 30o are complementary angles.
\n(ii)<\/strong> 5o and 85o are complementary angles.
\n6.<\/strong> Supplementary angles
\nTwo angles are supplementary when they add up to 180o.
\nExample<\/strong>
\n(i)<\/strong> 60o and 120o are supplementary angles.
\n(ii)<\/strong> 93 and 87 are supplementary angles.
\n7. Vertical angles<\/strong>
\nVertical angles are the angles opposite to each other when two lines cross. They are always equal.
\n8.<\/strong> Triangle<\/strong>
\nA triangle is a closed figure with three lines and three angles. These three angles always add up to 180o.
\n9.<\/strong> Right angle triangle<\/strong>
\nA triangle in which the measure of one angle equals 90o degree.
\n10.<\/strong> Isosceles triangle<\/strong>
\nAn isosceles triangle has two equal sides. The angles opposite to equal sides are also equal.
\n11.<\/strong> Right isosceles triangle<\/strong>
\nA right triangle that has 2 sides and 2 angles equal.
\nExplanation:<\/strong>
\na.<\/strong> In such a triangle, one angle is of 90o and other two are of 45o each.
\nb.<\/strong> This triangle satisfies the Pythagorean Theorem.
\n12.<\/strong> Scalene triangle
\nA triangle with all sides of different lengths and different angles is called a scalene triangle.
\n13. Acute angle triangle<\/strong>
\nA triangle in which measures of all angles are less than 90o.
\n14. Obtuse triangle<\/strong>
\nObtuse triangle is the one in which the measure of one triangle is greater than 90o.
\n15. Equilateral triangle<\/strong>
\nA triangle having three equal sides and three equal angles of 60o is called an equilateral triangle.<\/p>\n","protected":false},"excerpt":{"rendered":"

Angle An angle is a combination of \u201ctwo rays\u201d (half lines) with a common end point. a. Common end point = vertex b. Rays as the sides = legs or arms of the angle. Acute angle Less than 90o a. An angle whose measure is less than 90o is called an acute angle. b. Acute …<\/p>\n","protected":false},"author":8855,"featured_media":12281,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[31,8352],"tags":[8446,8449,8396,8447,8448],"_links":{"self":[{"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/posts\/12280"}],"collection":[{"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/users\/8855"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/comments?post=12280"}],"version-history":[{"count":0,"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/posts\/12280\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/media\/12281"}],"wp:attachment":[{"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/media?parent=12280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/categories?post=12280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.jworldtimes.com\/old-site\/wp-json\/wp\/v2\/tags?post=12280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}