Question

find the value of y.

Explanation:

Answer:

To solve for \( y \), we first need to find the value of \( x \) using the properties of parallel lines and transversals. The angles \( (13x - 33)^\circ \) and \( (10x)^\circ \) are corresponding angles (since the lines are parallel and cut by a transversal), so they are equal.

Step 1: Set up the equation for \( x \)

Since the corresponding angles are equal, we have:
\[
13x - 33 = 10x
\]

Step 2: Solve for \( x \)

Subtract \( 10x \) from both sides:
\[
13x - 10x - 33 = 0
\]
\[
3x - 33 = 0
\]
Add 33 to both sides:
\[
3x = 33
\]
Divide both sides by 3:
\[
x = \frac{33}{3} = 11
\]

Step 3: Find the measure of the angle \( (10x)^\circ \)

Substitute \( x = 11 \) into \( 10x \):
\[
10x = 10 \times 11 = 110^\circ
\]

Step 4: Use the linear pair or supplementary angle property for \( y \)

The angle \( (10x)^\circ = 110^\circ \) and \( (5y)^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \):
\[
110 + 5y = 180
\]

Step 5: Solve for \( y \)

Subtract 110 from both sides:
\[
5y = 180 - 110
\]
\[
5y = 70
\]
Divide both sides by 5:
\[
y = \frac{70}{5} = 14
\]

The value of \( y \) is \( \boxed{14} \).