document.write( "Question 1134178: If WXYZ is a rhombus and measure of angle YWZ = 43 degrees, find the measure of angle ZXW. \n" ); document.write( "

Algebra.Com's Answer #751509 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It is very easy to solve.\r\n" );
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document.write( "You are given that the angle YWZ is 43 degrees.\r\n" );
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document.write( "Hence, the angle ZWX has the measure which is TWO TIMES the measure of the angle YWZ, i.e. 86 degrees \r\n" );
document.write( "(since the diagonal WZY of the rhombus WXYZ bisects its angle W).\r\n" );
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document.write( "Next, since the angle ZWX (which is exactly the angle W at the vertex W of the rhombus) is 86 degrees,\r\n" );
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document.write( "then the angle WXY of the rhombus (which is the angle at the vertex X of the rhombus) is 180 - 86 = 94 degrees\r\n" );
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document.write( "It is because any two consecutive (= adjacent) interior angles of each rhombus are supplementary.\r\n" );
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document.write( "The last step is to notice that the angle ZXW is HALF of the angle WXY (diagonals of the rhombus bisect its angles).\r\n" );
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document.write( "Hence, the angle ZXW measure is 94/2 = 47 degrees.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On properties of rhombis, see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Diagonals of a rhombus are perpendicular\r
\n" ); document.write( "\n" ); document.write( "    - Diagonals of a rhombus bisect its angles\r
\n" ); document.write( "\n" ); document.write( "    - The length of diagonals of a rhombus\r
\n" ); document.write( "\n" ); document.write( "    - A circle inscribed in the rhombus\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve problems on the rhombus sides and diagonals measures - Examples \r
\n" ); document.write( "\n" ); document.write( "    - The length of diagonals of a rhombus \r
\n" ); document.write( "\n" ); document.write( "    - PROPERTIES OF RHOMBIS\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( "    GEOMETRY - YOUR ONLINE TEXTBOOK \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Properties of rhombis\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in GEOMETRY
\n" ); document.write( "https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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