document.write( "Question 148657: triangle ABC is inscribed in a circle. given that AB is a 40 degree arc and ABC is a 50 degree angle, find the sizes of the other arcs and angles in the figure. \r
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Algebra.Com's Answer #109001 by Edwin McCravy(20055) $\"\"$ $\"About$

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Triangle ABC is inscribed in a circle. given that AB is a 40 degree arc and ABC is a 50 degree angle, find the sizes of the other arcs and angles in the figure\r
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document.write( "Angle ACB is an inscribed angle, subtending a 40° arc.\r\n" );
document.write( "An inscribed angle has  the measure of its inscribed arc.\r\n" );
document.write( "Therefore angle ACB has measure 20°, so we write that in:\r\n" );
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document.write( "Since the three angles of any triangle total 180°, we find the \r\n" );
document.write( "remaining angle BAC by adding 50°+20°, getting 70°, then subtracting\r\n" );
document.write( "from 180° and getting 110°, so we write that in for angle BAC:\r\n" );
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document.write( "The inscribed angle at B is 50°. It subtends arc AC, and since it \r\n" );
document.write( "is  of the measure of its inscribed arc, the arc AC must be\r\n" );
document.write( "2x50° or 100°, so we write in 100° for arc AC:\r\n" );
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document.write( "The big major arc going clockwise from B around to C is subtended by \r\n" );
document.write( "the 110° angle at A.  And since it is  of the measure of its \r\n" );
document.write( "inscribed arc, the large major arc BC must be 2x110° or 220°, so we \r\n" );
document.write( "write in 220° for major arc BC, going clockwise from B around to C:\r\n" );
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document.write( "Notice as a partial check that the three arcs have sum 360°.\r\n" );
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document.write( "minor are AB =  40²\r\n" );
document.write( "minor arc AC = 100°\r\n" );
document.write( "major arc BC = 220°\r\n" );
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document.write( "       total = 360°\r\n" );
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document.write( "Edwin

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