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}
.