Question

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

Explanation:

Step1: Identify angle relationship

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

Step2: Solve for \( x \)

Subtract 5 from both sides: \( 5x = 115 - 5 = 110 \).
Divide by 5: \( x = \frac{110}{5} = 22 \).

Answer:

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