practice:
4 in the figure, the lines are parallel what is the relationship given?
o supplementary
o vertical
acute angle:_____
obtuse angle:_____

Question

Accepted Answer

# Explanation:
## Step1: Identify the relationship
Since the lines are parallel, and the two angles are consecutive interior angles (same - side interior angles), they are supplementary. That is, $(23x - 5)+(21x + 7)=180$

## Step2: Solve for $x$
$$
\begin{align*}
23x-5 + 21x+7&=180\
44x+2&=180\
44x&=180 - 2\
44x&=178\
x&=\frac{178}{44}=\frac{89}{22}\approx4.045
\end{align*}
$$

## Step3: Find the measure of the angles
- For the angle $21x + 7$:
$$
\begin{align*}
21\times\frac{89}{22}+7&=\frac{1869}{22}+7\
&=\frac{1869 + 154}{22}\
&=\frac{2023}{22}\approx91.95^{\circ}
\end{align*}
$$
- For the angle $23x - 5$:
$$
\begin{align*}
23\times\frac{89}{22}-5&=\frac{2047}{22}-5\
&=\frac{2047-110}{22}\
&=\frac{1937}{22}\approx88.05^{\circ}
\end{align*}
$$

# Answer:
Acute Angle: $23x - 5\approx88.05^{\circ}$
Obtuse Angle: $21x + 7\approx91.95^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the relationship

Step2: Solve for \(x\)

Step3: Find the measure of the angles

Answer: