# Khan/khan-exercises

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randomQuadAngles.trapezoid() randRange( 0, 3 ) ANSWER_POS % 2 === 0 ? ( ANSWER_POS + 3 ) % 4 : ( ANSWER_POS + 1 ) % 4 function(){ var a = [ "", "","" ,"" ]; a[ ANSWER_POS ] = "x"; a[ SHOWN_POS ] = ANGLES[ SHOWN_POS ] + "^{\\circ}"; return a; }()
What is the value of the angle marked with "x" ?
init({ range: [ [-1, 12 ], [ -8, -1 ] ] }) var q = new Quadrilateral( [ 3.5, -7 ], ANGLES, randRange(0, 1 ) + 0.5, "", 3 ); q.boxOut( [ [ [ 0, -10 ], [ 0, 10 ] ] ], [ 0.7, 0 ] ); q.boxOut( [ [ [ 11, -10 ], [ 11, 10 ] ] ], [ -0.7, 0 ] ); q.draw(); q.labels = { "angles" : ANG_LABELS, "sides" : \$.map( \$.map( q.sides, lineLength ), function( x ){ return x.toFixed( 1 ); } ) }; q.drawLabels();

This figure is a trapezoid.

The angles of a trapezoid side are supplementary.

ANGLES[ SHOWN_POS ] + x = 180

x = 180 - ANGLES[ SHOWN_POS ]

This figure is an isosceles trapezoid.

The angles of bases of an isosceles trapezoid are equal.

Therefore, the angle x is also ANGLES[ SHOWN_POS ]

Opposite angles of a parallelogram are equal.

Therefore, the angle x is also ANGLES[ SHOWN_POS ]

Adjacent angles of a parallelogram are supplementary.

ANGLES[ SHOWN_POS ] + x = 180

x = 180 - ANGLES[ SHOWN_POS ]

init({ range: [ [-1, 13 ], [ -8, -1 ] ] }) var q = new Quadrilateral( [ 3.5, -7 ], ANGLES, 1, "", 3 ); q.boxOut( [ [ [ 0, -10 ], [ 0, 10 ] ] ], [ 0.7, 0 ] ); q.boxOut( [ [ [ 12, -10 ], [ 12, 10 ] ] ], [ -0.7, 0 ] ); q.draw(); q.labels = { "angles" : ANG_LABELS, "sides" : \$.map( \$.map( q.sides, lineLength ), function( x ){ return x.toFixed( 1 ); } ) }; q.drawLabels();

This quadrilateral is a rhombus, because it has all sides equal.

Opposite angles of a rhombus are equal.

Therefore, the angle x is also ANGLES[ SHOWN_POS ]

This quadrilateral is a rhombus, because it has all sides equal.

Adjacent angles of a rhombus are supplementary.

ANGLES[ SHOWN_POS ] + x = 180

x = 180 - ANGLES[ SHOWN_POS ]