document.write( "Question 1190527: Solve the problem. \r
\n" ); document.write( "\n" ); document.write( "One of the parallel sides of an isosceles trapezoid inscribed in circle intercepts an arc with a measure of 80 degrees, while the other side is a diameter. Find the measure of the angle formed by the diagonal of the trapezoid. \n" ); document.write( "

Algebra.Com's Answer #822219 by ikleyn(52908) $\"\"$ $\"About$

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\n" ); document.write( "One of the parallel sides of an isosceles trapezoid inscribed in circle
\n" ); document.write( "intercepts an arc with a measure of 80 degrees, while the other side is a diameter.
\n" ); document.write( "Find the measure of the angle formed by the diagonal of the trapezoid.
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document.write( "Make a sketch.\r\n" );
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document.write( "Let the trapezoid be ABCD, with the diameter of the circle AB as the longer base and\r\n" );
document.write( "the chord CD as the shorter base.\r\n" );
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document.write( "Let P be the intersection point of diagonals AC and BD of the trapezoid.\r\n" );
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document.write( "They want you find the angle APB.\r\n" );
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document.write( "Notice that the arcs AD and BC each has the measure of   = 50 degrees,\r\n" );
document.write( "since the trapezoid is isosceles.\r\n" );
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document.write( "So, the angles BAC and ABC have measures half of 50 degrees each, i.e. 25 degrees,\r\n" );
document.write( "since they are inscribed angles leaning the arcs of 50 degrees.\r\n" );
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document.write( "Thus the triangle APB has the base angles PAB and PBA of 25 degrees each.\r\n" );
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document.write( "It implies that the angle APB is  (180-25-25) = 130 degrees.\r\n" );
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document.write( "So, the problem is just solved.\r\n" );
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document.write( "The obtuse angle between the diagonals of the trapezoid is 130 degrees;\r\n" );
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document.write( "the corresponding acute angle is 180-130 = 50 degrees.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "From the context, the meaning of the problem is MORE THAN OBVIOUS, so you, the reader, \r
\n" ); document.write( "\n" ); document.write( "feel free to use the solution in my post, disregarding critical notices by @greenestamps.\r
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\n" ); document.write( "\n" ); document.write( "By the way and in addition, the meaning of the problem is CLEARLY DECIPHERED in my solution, \r
\n" ); document.write( "\n" ); document.write( "so any doubts are excessive . . . \r
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