Question

1. find the value of x so that ℓ ∥ m. (7x + 15)° ℓ m 25° n

Explanation:

Step1: Identify the angle relationship

Since \( \ell \parallel m \) and \( n \) is a transversal, the angle \( (7x + 15)^\circ \) and the \( 25^\circ \) angle are supplementary (they form a linear pair or are same - side exterior/interior angles? Wait, actually, looking at the diagram, the \( (7x + 15)^\circ \) and the \( 25^\circ \) angle are supplementary because they are adjacent and form a linear pair when \( \ell\parallel m \). So \( (7x + 15)+25 = 180 \).

Step2: Solve the equation

First, simplify the left - hand side of the equation:
\( 7x+15 + 25=7x + 40 \)
So the equation becomes \( 7x+40 = 180 \)
Subtract 40 from both sides: \( 7x=180 - 40=140 \)
Divide both sides by 7: \( x=\frac{140}{7}=20 \)

Answer:

\( x = 20 \)