Question

given the following figure, solve for y. (7y + 27)° figure: two parallel horizontal lines cut by a transversal; one angle is 125°, the other is (7y + 27)° options: y = 4, y = 14, y = 22, y = 34

Explanation:

Step1: Identify angle relationship

The angle \( (7y + 27)^\circ \) and \( 125^\circ \) are corresponding angles (since the lines are parallel and cut by a transversal), so they are equal. Thus, we set up the equation:
\( 7y + 27 = 125 \)

Step2: Solve for y

Subtract 27 from both sides:
\( 7y = 125 - 27 \)
\( 7y = 98 \)

Divide both sides by 7:
\( y = \frac{98}{7} \)
\( y = 14 \)

Answer:

\( y = 14 \) (corresponding to the option "y = 14")