Question

two parallel lines are crossed by a transversal. what is the value of x? (5x+5)° and 115° angle in diagram. options: x=12, x=14, x=22, x=24

Explanation:

Step1: Identify angle relationship

Since lines \( b \) and \( c \) are parallel, and \( a \) is a transversal, the angle \( (5x + 5)^\circ \) and \( 115^\circ \) are corresponding angles (or alternate interior angles, depending on position), so they are equal. Thus, we set up the equation:
\( 5x + 5 = 115 \)

Step2: Solve for \( x \)

Subtract 5 from both sides:
\( 5x = 115 - 5 \)
\( 5x = 110 \)

Divide both sides by 5:
\( x = \frac{110}{5} \)
\( x = 22 \)

Answer:

\( x = 22 \) (corresponding to the option \( x = 22 \))