Question

6 find the value of y.
8 find the value of y.

Explanation:

Step1: Find the value of \(x\)

Since \(9x + 42\) and \(15x\) are supplementary angles (they form a linear pair), we have the equation:

$$9x+42 + 15x=180$$

Combine like - terms:

$$24x+42 = 180$$

Subtract 42 from both sides:

$$24x=180 - 42$$

$$24x=138$$

Divide both sides by 24:

$$x=\frac{138}{24}=\frac{23}{4}$$

Step2: Use the property of parallel lines (corresponding angles)

The angle \(15x\) and \(4y-13\) are corresponding angles (assuming the lines are parallel).
First, find the value of \(15x\):

$$15x=15\times\frac{23}{4}=\frac{345}{4}$$

Since \(15x = 4y-13\), we substitute \(15x\):

$$\frac{345}{4}=4y - 13$$

Add 13 to both sides:

$$4y=\frac{345}{4}+13=\frac{345 + 52}{4}=\frac{397}{4}$$

Divide both sides by 4:

$$y=\frac{397}{16}=24.8125$$

Answer:

\(y = 24.8125\)