12.
(7y - 20)° (5x - 38)°
(3x - 4)°

Question

Accepted Answer

# Explanation:
## Step1: Use the property of parallel lines (alternate - interior angles)
Since $l\parallel m$, we know that $(7y - 20)^{\circ}=(3x - 4)^{\circ}$ (alternate - interior angles). Also, by the property of angles on a straight line (the sum of angles formed by a transversal with two parallel lines and a right - angle in between), we have $(5x - 38)+90+(3x - 4)=180$ (linear - pair of angles).
First, simplify the equation $(5x - 38)+90+(3x - 4)=180$:
$$
\begin{align*}
5x-38 + 90+3x-4&=180\
(5x + 3x)+(-38-4 + 90)&=180\
8x+48&=180\
8x&=180 - 48\
8x&=132\
x&=\frac{132}{8}=\frac{33}{2}=16.5
\end{align*}
$$
## Step2: Substitute $x$ into the equation for $y$
Substitute $x = 16.5$ into $7y-20=3x - 4$.
$$
\begin{align*}
7y-20&=3\times16.5-4\
7y-20&=49.5-4\
7y-20&=45.5\
7y&=45.5 + 20\
7y&=65.5\
y&=\frac{65.5}{7}=\frac{131}{14}\approx9.36
\end{align*}
$$

# Answer:
$x = 16.5$, $y=\frac{131}{14}\approx9.36$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Use the property of parallel lines (alternate - interior angles)

Step2: Substitute \(x\) into the equation for \(y\)

Answer: