document.write( "Question 304848: An isosceles triangle has one 25 degree angle and the base angles are each (5x) classify the triangle by its angle measures \n" ); document.write( "
Algebra.Com's Answer #218316 by Edwin McCravy(20060)\"\" \"About 
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An isosceles triangle has one 25 degree angle and the base angles are each (5x) classify the triangle by its angle measures.
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document.write( "This problem does not tell us that the vertex angle is the\r\n" );
document.write( "angle that is 25°.  Each of the base angles could be 25° as\r\n" );
document.write( "well.\r\n" );
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document.write( "So there are two solutions:\r\n" );
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document.write( "Case 1: The vertex angle is the only one which is 25°,\r\n" );
document.write( "and the base angles are 5x each:\r\n" );
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document.write( "In this case the sum of all three angle measures must equal 180°,\r\n" );
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document.write( "so we have the equation:\r\n" );
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document.write( "25° + 5x + 5x = 180°\r\n" );
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document.write( "    25° + 10x = 180°\r\n" );
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document.write( "          10x = 180° - 25°\r\n" );
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document.write( "          10x = 155°\r\n" );
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document.write( "            x = 15.5° \r\n" );
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document.write( "So since each of the base angles have measure 5x in this\r\n" );
document.write( "case, each base angle is 5(15.5°) or 77.5°, so the\r\n" );
document.write( "three angles are 25°, 77.5° and 77.5°.\r\n" );
document.write( "This angles is an acute isosceles triangle because\r\n" );
document.write( "it has three acute angles, which means they are all\r\n" );
document.write( "less than 90°.\r\n" );
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document.write( "But we also have\r\n" );
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document.write( "Case 2: The base angles have measure 5x each:\r\n" );
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document.write( "In this case the vertex angle = 180° - 25° - 25° = 180° - 50° = 130°\r\n" );
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document.write( "The angles are 25°, 25°, 130°\r\n" );
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document.write( "So since one of the angles has measure 130° in this\r\n" );
document.write( "case, this triangle is an obtuse isosceles triangle because\r\n" );
document.write( "it has one obtuse angle, which means its measure is \r\n" );
document.write( "greater than 90°.\r\n" );
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document.write( "Notice that a triangle only needs ONE obtuse angles to be\r\n" );
document.write( "classified as an obtuse triangle, but it requires THREE\r\n" );
document.write( "acute angles to be classified as an acute triangle.  The\r\n" );
document.write( "reason is that EVERY triangle has at least two acute\r\n" );
document.write( "angles anyway!\r\n" );
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document.write( "5x = 25°\r\n" );
document.write( " x = 5°\r\n" );
document.write( "     \r\n" );
document.write( "We didn't have to find x for this case, but as we see it is 5°,\r\n" );
document.write( "in case you had been asked for x.\r\n" );
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document.write( "Edwin
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