Question

find the value of x for which d||m. (2x−27)° 87° d m x=□ (simplify your answer. type an integer or a fraction.)

Explanation:

Answer:

To determine the value of \( x \) for which \( d \parallel m \), we use the property of alternate interior angles (or corresponding angles, depending on the configuration). When two parallel lines are cut by a transversal, alternate interior angles are equal.

Here, the angle \( (2x - 27)^\circ \) and \( 87^\circ \) are alternate interior angles (or corresponding angles, depending on the diagram). So we set them equal:

\[
2x - 27 = 87
\]

Solving for \( x \):

1. Add 27 to both sides:

\[
2x = 87 + 27
\]
\[
2x = 114
\]

1. Divide both sides by 2:

\[
x = \frac{114}{2}
\]
\[
x = 57
\]

So the value of \( x \) is \( \boxed{57} \).