Given
\qquad m LARGE_ANGLE = largeAngle^\circ
\qquad m LARGE_ANGLE is a straight angle.
\qquad \overline{OA}\perp\overline{OC}
\qquad m ANGLE_ONE = COEF_1x + CONST_1^\circ
\qquad m ANGLE_TWO = COEF_2x + CONST_2^\circ
Find mANSWER[0]:
{}^{\circ}
From the diagram, we see that together \blue{ANGLE_TOP} and \green{ANGLE_BOT} form \purple{LARGE_ANGLE}, so
\qquad \blue{mANGLE_TOP} + \green{mANGLE_BOT} = \purple{mLARGE_ANGLE}.
Since LARGE_ANGLE is a straight angle,
we know \purple{mLARGE_ANGLE = 180^\circ}.
Since we are given that \overline{OA}\perp\overline{OC},
we know \purple{mLARGE_ANGLE = 90^\circ}.
Substitute in the expressions that were given for each measure:
\qquad \blue{COEF_1x + CONST_1^\circ} + \green{COEF_2x + CONST_2^\circ} =
\purple{largeAngle^\circ}.
\qquad \blue{COEF_2x + CONST_2^\circ} + \green{COEF_1x + CONST_1^\circ} =
\purple{largeAngle^\circ}.
Combine like terms:
\qquadCOEF_1 + COEF_2x + CONST_1 + CONST_2^\circ = largeAngle^\circ.
Subtract CONST_1 + CONST_2^\circ from both sides:
Add -(CONST_1 + CONST_2)^\circ to both sides:
\qquadCOEF_1 + COEF_2x = largeAngle - CONST_1 - CONST_2^\circ.
Divide both sides by COEF_1 + COEF_2 to find x:
\qquad \pink{x = X^\circ}.
Substitute \pink{X}^\circ for \pink{x} in the expression that was given for
\green{mANSWER[0]}:
\qquad \green{mANSWER[0] =
ANSWER[1](}\pink{X^\circ}\green{) + ANSWER[2]^\circ}.
Substitute \pink{X^\circ} for \pink{x} in the expression that was given for
\blue{mANSWER[0]}:
\qquad \blue{mANSWER[0] =
ANSWER[1](}\pink{X^\circ}\blue{) + ANSWER[2]^\circ}.
Simplify:
\qquad \green{mANSWER[0]^\circ = ANSWER[1] * X^\circ + ANSWER[2]^\circ}.
Simplify:
\qquad \blue{mANSWER[0]^\circ = ANSWER[1] * X^\circ + ANSWER[2]^\circ}.
So \green{mANSWER[0] = ANSWER[1] * X + ANSWER[2]^\circ}.
So \blue{mANSWER[0] = ANSWER[1] * X + ANSWER[2]^\circ}.