# Khan/khan-exercises

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 Complementary and supplementary angles
randFromArray([ ["O", "A", "B", "C"], ["O", "L", "M", "N"], ["P", "Q", "R", "S"] ]) randRange(1, 89) "\\angle " + A + O + B "\\angle " + B + O + C shuffle([ ANGLE_BOT, ANGLE_TOP ])

If \angle A + O + C is a right angle and m ANGLE_ONE = ANGLE^\circ, what is m ANGLE_TWO?

init({ range: [ [-2, 7], [-1, 6] ], scale: 40 }); var DISP_ANGLE = Math.min( Math.max( 10, ANGLE ), 80 ); if ( ANGLE_ONE !== ANGLE_BOT ) { DISP_ANGLE = 90 - DISP_ANGLE; arc( [ 0, 0 ], 1, DISP_ANGLE, 90 ); DISP_ANGLE *= PI / 180; label( [ 2 * cos( DISP_ANGLE + ( PI / 2 - DISP_ANGLE) / 2 ) + 0.125, 2 * sin( DISP_ANGLE + ( PI / 2 - DISP_ANGLE) / 2 ) + 0.5 ], ANGLE + "^\\circ" ); } else { arc( [ 0, 0 ], 1, 0, DISP_ANGLE ); DISP_ANGLE *= PI / 180; label( [ 2 * cos( DISP_ANGLE / 2 ) + 0.65 , 2 * sin( DISP_ANGLE / 2 )], ANGLE + "^\\circ" ); } path([ [0, 5], [0, 0], [5, 0] ]); path([ [0, 0], [5 * cos( DISP_ANGLE ), 5 * sin( DISP_ANGLE )] ]); label( [0, 0], O, "below left" ); label( [5, 0], A, "right" ); label( [0, 5], C, "above" ); // somewhat ick to make it look nice label( [5.4 * cos( DISP_ANGLE ), 5.4 * sin( DISP_ANGLE )], B );

NOTE: Angles not necessarily drawn to scale.

90 - ANGLE \Large{^\circ}

From the diagram, we see that ANGLE_BOT and ANGLE_TOP are complementary angles.

Therefore, m ANGLE_BOT + m ANGLE_TOP = 90^\circ.

Thus, m ANGLE_TWO = 90^\circ - m ANGLE_ONE = 90^\circ - ANGLE^\circ = 90 - ANGLE^\circ.

randFromArray([ ["O", "A", "B", "C"], ["O", "L", "M", "N"], ["P", "Q", "R", "S"] ]) randRange(1, 179) "\\angle " + A + O + B "\\angle " + B + O + C shuffle([ ANGLE_BOT, ANGLE_TOP ])

If m \angle A + O + C = 180^\circ and m ANGLE_ONE = ANGLE^\circ, what is m ANGLE_TWO?

init({ range: [ [-7, 7], [-1, 6] ], scale: 40 }); var DISP_ANGLE = Math.min( Math.max( 10, ANGLE ), 170 ); if ( ANGLE_ONE !== ANGLE_BOT ) { DISP_ANGLE = 180 - DISP_ANGLE; arc( [ 0, 0 ], 1, DISP_ANGLE, 180 ); DISP_ANGLE *= PI / 180; label( [ 2 * cos( DISP_ANGLE + ( PI - DISP_ANGLE) / 2 ) - .5, 2 * sin( DISP_ANGLE + ( PI - DISP_ANGLE) / 2 )], ANGLE + "^\\circ" ); } else { arc( [ 0, 0 ], 1, 0, DISP_ANGLE ); DISP_ANGLE *= PI / 180; label( [ 2 * cos( DISP_ANGLE / 2 ) + .5 , 2 * sin( DISP_ANGLE / 2 )], ANGLE + "^\\circ" ); } path([ [-5, 0], [5, 0] ]); path([ [0, 0], [5 * cos( DISP_ANGLE ), 5 * sin( DISP_ANGLE )] ]); label( [0, 0], O, "below" ); label( [5, 0], A, "right" ); label( [-5, 0], C, "left" ); // somewhat ick to make it look nice label( [5.35 * cos( DISP_ANGLE ), 5.35 * sin( DISP_ANGLE )], B );

NOTE: Angles not necessarily drawn to scale.

180 - ANGLE \Large{^\circ}

From the diagram, we see that ANGLE_BOT and ANGLE_TOP are supplementary angles.

Therefore, m ANGLE_BOT + m ANGLE_TOP = 180^\circ.

Thus, m ANGLE_TWO = 180^\circ - m ANGLE_ONE = 180^\circ - ANGLE^\circ = 180 - ANGLE^\circ.