Question

find the value of the variables in the given figure.

x = 28, y =

Explanation:

Step1: Find the value of \( x \)

Since \( 5x\) and \( 40^{\circ}\) are supplementary angles (they form a linear pair), we have the equation \( 5x+40 = 180\).
Subtract \( 40\) from both sides: \( 5x=180 - 40\), so \( 5x = 140\).
Divide both sides by \( 5\): \( x=\frac{140}{5}=28\).

Step2: Find the value of \( y \)

The angle \( (3y - 1)^{\circ}\) and \( 5x^{\circ}\) are corresponding angles (because the lines are parallel). Since \( x = 28\), then \( 5x=140\).
So, \( 3y-1=140\).
Add \( 1\) to both sides: \( 3y=140 + 1\), so \( 3y=141\).
Divide both sides by \( 3\): \( y=\frac{141}{3}=47\).

Answer:

\( x = 28\), \( y = 47\)