If m \angle A + O + C = 180^\circ and m ANGLE_ONE = ANGLE^\circ, what is m ANGLE_TWO, in degrees?
init({
range: [ [-7, 7], [-2, 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 );
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.