The two horizontal lines are parallel, and there is a third line that intersects them as shown below.
Solve for x
:
SOLUTION
Alternate interior angles are equal to one another. Watch this video to understand why.
The \color{BLUE}{\text{blue angle}}
and the \color{ORANGE}{\text{orange angle}}
are alternate interior angles. Therefore, we can set them equal to one another.
\color{BLUE}{Ax + B} = \color{ORANGE}{Cx + D}
Subtract \color{PINK}{Cx}
from both sides.
(Ax + B) \color{PINK}{- Cx} = (Cx + D) \color{PINK}{- Cx}
A - Cx + B = D
B > 0 ? "Subtract" : "Add" \color{PINK}{abs(B)}
B > 0 ? "from" : "to" both sides.
(A - Cx + B) \color{PINK}{+ -B} = D \color{PINK}{+ -B}
A - Cx = D - B
Divide both sides by \color{PINK}{A - C}
.
\dfrac{A - Cx}{\color{PINK}{A - C}} = \dfrac{D - B}{\color{PINK}{A - C}}
Simplify.
x = SOLUTION
Subtract \color{PINK}{Ax}
from both sides.
(Ax + B) \color{PINK}{- Ax} = (Cx + D) \color{PINK}{- Ax}
B = C - Ax + D
D > 0 ? "Subtract" : "Add" \color{PINK}{abs(D)}
D > 0 ? "from" : "to" both sides.
B \color{PINK}{+ -D} = (C - Ax + D) \color{PINK}{+ -D}
B - D = C - Ax
Divide both sides by \color{PINK}{C - A}
.
\dfrac{B - D}{\color{PINK}{C - A}} = \dfrac{C - Ax}{\color{PINK}{C - A}}
Simplify.
SOLUTION = x