Lesson Introduction and Properties of Angles
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Geometry: Angles, complementary, supplementary angles
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In this lesson we are going to discuss the concept of Angle, types of angles and its properties. We will start with the basic understanding of an angle and will look into the issues related to the representation of angles and type of angles. <b><A HREF=Angle.wikipedia>Angle</A>:</b> An Angle is the amount of rotation about the point of intersection (vertex) of two lines in order to make one line into correspondence with other. An Angle is denoted by script {{{theta}}}. Angles are usually measured in <b>degrees</b> (denoted degrees), <b>radians</b> (denoted rad, or without a unit), or sometimes <b>gradians</b> (denoted grad). According to the sign convention the <b>Anticlockwise</b> rotation is considered to be positive and <b>Clockwise</b> rotation is considered to be negative. <b>In this lesson all the angles are assumed to be measured by Anticlockwise rotation.</b> <b>Full Angle:</b> If we consider a circle then the angle swiped in a full rotation of a circle is called Full Angle. In the full rotation we can relate three measures of an angle as: {{{360 degrees = 2*pi = 400 grad}}} {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( 2, 2,4.5,2)), locate( 1.7,3, 360 ),red(circle( 2, 2,.4 )),circle( 2,2,2.5))}}} <b><A HREF=Straight_angle.wikipedia>Straight Angle</A>:</b> Angle swiped in a half rotation of a circle is called Straight Angle. Its measurement is 180 degrees. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( -.5, 2,4.5,2)), locate( 2,3, 180),red(circle( 2, 2,.1 )),circle( 2,2,2.5))}}} <b><A HREF=Right_angle.wikipedia>Right Angle</A>:</b> Angle swiped in a quarter rotation of a circle is called right Angle. Its measurement is 90 degrees. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( 2, 2,4.5,2)) , green(line( 2, 2,2,4)), locate( 2.5,2.5, 90),red(circle( 2, 2,.1 )),circle( 2,2,2.5))}}} <b><A HREF=Acute_angle.wikipedia>Acute Angle</A>:</b> Angle swiped in less than a quarter rotation of a circle is called Acute Angle. Its measurement varies from 0 to 90 degrees. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( 2, 2,4.5,2)) , green(line( 2, 2,3.25,3.65)), locate( 2.5,2.5,A),locate( 5,5,A<90),red(circle( 2, 2,.1 )),circle( 2,2,2.5))}}} <b><A HREF=Obtuse_angle.wikipedia>Obtuse Angle</A>:</b> Angle swiped between quarter and half rotation of a circle is called Obtuse Angle. Its measurement varies from 90 to 180 degrees. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( 2, 2,4.5,2)) , green(line( 2, 2,.75,3.65)), locate( 3.5,5,90<A<180),locate( 2,2.6,A),red(circle( 2, 2,.1 )),circle( 2,2,2.5))}}} <b><A HREF=Reflex_angle.wikipedia>Reflex Angle</A>:</b> Angle swiped between half and full rotation of a circle is called Reflex Angle. Its measurement varies from 180 to 360 degrees. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, green(line( 2, 2,4.5,2)) , green(line( 2, 2,.75,.35)), locate( 3,5,180<A<360),locate( 1.5,2.6,A),red(circle( 2, 2,.1 )),circle( 2,2,2.5))}}} There are certain nomenclature which uses more than one angle. i.e. Complementary Angles and Supplementary Angles <b><A HREF=Complementary_angle.wikipedia>Complementary Angles</A>:</b> Angle A and B are such that {{{A + B = 90}}} then A and B are said to be Complementary Angles. In other words the A and B are complementary angles if they produce a right angle when combined. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, line( 0, 0, 0, 4 ),line( 0, 0, 5, 0 ), line( 0, 0, 3, 3.5 ),locate( .3, 1.4, B ),locate( .7, .7, A ),locate( 3.2,5,A+B=90))}}} <b><A HREF=Supplementary_angle.wikipedia>Supplementary Angles</A>:</b> Angle A and B are such that {{{A + B = 180}}} then A and B are said to be Supplementary Angles. In other words the A and B are Supplementary angles if they produce a straight angle when combined. {{{drawing( 160, 160, -0.5, 6.5, -0.5, 5.0, line( 0, 0, 6, 0 ), line( 3, 0, 1.5, 2.5),red(circle( 3, 0,.1 )),locate( 3.4, .7, A ),locate( 2,.7, B ),locate( 3.2,5,A+B=180))}}} For more information about Angles refer to <A HREF=Angle.wikipedia>wikipedia</A>.
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