find the value of y. (14y - 4)° (3x + 11)° (x + 21)°

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Accepted Answer

# Explanation:
## Step1: Find the value of $ x $
Since $ (3x + 11)^{\circ} $ and $ (x + 21)^{\circ} $ are supplementary angles (they form a linear pair), we have the equation:
$$
\begin{align*}
(3x + 11)+(x + 21)&=180\
4x+32&=180\
4x&=180 - 32\
4x&=148\
x&=\frac{148}{4}\
x&=37
\end{align*}
$$
## Step2: Find the value of $ y $
$ (14y - 4)^{\circ} $ and $ (3x + 11)^{\circ} $ are corresponding angles (assuming the two lines are parallel). Substitute $ x = 37 $ into $ 3x+11 $:
$ 3x+11=3\times37 + 11=111 + 11=122 $
Then set $ 14y-4 = 122 $
$$
\begin{align*}
14y-4&=122\
14y&=122 + 4\
14y&=126\
y&=\frac{126}{14}\
y&=9
\end{align*}
$$

# Answer:
$ y = 9 $

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Explanation:

Step1: Find the value of \( x \)

Step2: Find the value of \( y \)

Answer: