document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204851>Question 1204851</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the diagram on the right, AB is the diameter of the circle, and E is the<BR>\n" );
document.write( "centre. Find the measure of angle D, in degrees. \r<BR>\n" );
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document.write( "https://ibb.co/SxjJWg5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841387 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
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document.write( "Because segment AB is a diameter, triangle ABC is a right triangle with C = 90 degrees. This is due to Thale's Theorem. <BR>\n" );
document.write( "It's the special case of the Inscribed Angle Theorem.\r<BR>\n" );
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document.write( "Acute angle B of triangle ABC is 90-A = 90-32 = 58 degrees.<BR>\n" );
document.write( "Since angle ABC = 58, so is angle DEB because of the Alternate Interior Angles Theorem. <BR>\n" );
document.write( "Note the parallel line markers on BC and DE.<BR>\n" );
document.write( "Those are indeed parallel line markers and not vector symbols.\r<BR>\n" );
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document.write( "angleDEB + angleAED = 180<BR>\n" );
document.write( "angleAED = 180 - angleDEB<BR>\n" );
document.write( "angleAED = 180 - 58<BR>\n" );
document.write( "angleAED = 122<BR>\n" );
document.write( "This represents angle E of triangle AED.\r<BR>\n" );
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document.write( "Focus on triangle AED. <BR>\n" );
document.write( "This is isosceles due to radii ED = EA<BR>\n" );
document.write( "The congruent base angles A and D are opposite the congruent sides ED and EA respectively.\r<BR>\n" );
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document.write( "For any triangle, the 3 inside angles always add to 180 degrees.<BR>\n" );
document.write( "A+E+D = 180<BR>\n" );
document.write( "x+122+x = 180<BR>\n" );
document.write( "2x+122 = 180<BR>\n" );
document.write( "2x = 180-122<BR>\n" );
document.write( "2x = 58<BR>\n" );
document.write( "x = 58/2<BR>\n" );
document.write( "x = 29<BR>\n" );
document.write( "Therefore, <font color=red>angle D is 29 degrees.</font>\r<BR>\n" );
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document.write( "Notice how interior angles A and D add to exterior angle DEB. <BR>\n" );
document.write( "Refer to the Remote Interior Angle Theorem for more info\r<BR>\n" );
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document.write( "The Remote Interior Angle Theorem is useful to help quickly prove the Inscribed Angle Theorem.\r<BR>\n" );
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document.write( "Edit<BR>\n" );
document.write( "Greenestamps' answer is shockingly bad. \r<BR>\n" );
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document.write( "It's very hand-wavy, and doesn't mention any theorems he used. <BR>\n" );
document.write( "Both are *really* bad practices in mathematics. <BR>\n" );
document.write( "Advice to students: Do NOT follow what Greenestamps did.<BR>\n" );
document.write( "At least you know what not to do.\r<BR>\n" );
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document.write( "Not to mention there's a strange contradiction when he mentioned \"arc BC is 64 degrees, arcs BC and CF are each 58 degrees\". <BR>\n" );
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