Question

in the figure shown below, if line m is parallel to line n, then find the value of x. (2x - 10)° and (65 - x)° angles are formed by a transversal intersecting parallel lines m and n. x = blank

Explanation:

Step1: Identify the angle relationship

Since line \( m \) is parallel to line \( n \), the two given angles are alternate interior angles, so they are equal. Thus, we set up the equation:
\( 2x - 10 = 65 - x \)

Step2: Solve for \( x \)

Add \( x \) to both sides of the equation:
\( 2x + x - 10 = 65 - x + x \)
\( 3x - 10 = 65 \)

Add 10 to both sides:
\( 3x - 10 + 10 = 65 + 10 \)
\( 3x = 75 \)

Divide both sides by 3:
\( \frac{3x}{3} = \frac{75}{3} \)
\( x = 25 \)

Answer:

\( 25 \)