Question

solve for x.

x =
submit
work it out
not feeling ready yet? these can help:

Explanation:

Step1: Identify angle relationship

Since \( EF \parallel GH \) and \( CD \) is a transversal, \( \angle EIC \) and the angle adjacent to \( 73^\circ \) (vertical or corresponding) are equal. Wait, actually, \( \angle EIC=(7x - 4)^\circ \) and the angle \( \angle HJD = 73^\circ \), and since \( EF\parallel GH \), \( \angle EIC \) and \( \angle HJD \) are equal? Wait, no, actually, \( \angle EIC \) and the angle that is equal to \( 73^\circ \) (corresponding angles) because \( EF \parallel GH \) and \( CD \) is transversal. Wait, \( \angle EIC=(7x - 4)^\circ \) and \( \angle HJD = 73^\circ \), and since \( EF \parallel GH \), \( \angle EIC=\angle HJD \)? Wait, no, maybe \( \angle EIC \) and \( \angle HJD \) are corresponding angles, so they are equal. Wait, let's check: \( EF \) and \( GH \) are parallel, \( CD \) is transversal, so \( \angle EIC \) (at \( I \)) and \( \angle HJD \) (at \( J \)) are corresponding angles, so they are equal. So \( 7x - 4=73 \)? Wait, no, wait, maybe I made a mistake. Wait, \( \angle EIC \) is equal to the angle that is vertical to the angle adjacent to \( 73^\circ \). Wait, no, let's see: \( \angle IJG \) and \( \angle HJD \) are supplementary? No, \( \angle HJD = 73^\circ \), so the angle \( \angle IJ G= 180 - 73 = 107 \)? No, wait, maybe \( EF \parallel GH \), so \( \angle EIC \) and \( \angle GJI \) are equal? Wait, no, let's start over.

Wait, the lines \( EF \) and \( GH \) are parallel, and \( CD \) is a transversal. So \( \angle EIC \) (which is \( (7x - 4)^\circ \)) and the angle \( \angle HJD = 73^\circ \) – are they corresponding angles? Let's see the positions: \( E \) and \( G \) are on the left, \( F \) and \( H \) on the right. So \( \angle EIC \) is at the top intersection ( \( I \)) between \( EF \) and \( CD \), and \( \angle HJD \) is at the bottom intersection ( \( J \)) between \( GH \) and \( CD \). So they are corresponding angles, so they should be equal. So \( 7x - 4 = 73 \)? Wait, no, that would give \( 7x=77 \), \( x = 11 \), but let's check. Wait, maybe \( \angle EIC \) and \( \angle HJD \) are equal because of parallel lines and transversal (corresponding angles). So:

\( 7x - 4 = 73 \)

Step2: Solve for x

Add 4 to both sides:

\( 7x - 4 + 4 = 73 + 4 \)

\( 7x = 77 \)

Divide both sides by 7:

\( x=\frac{77}{7}=11 \)

Wait, but wait, maybe I mixed up the angles. Wait, another approach: \( \angle EIC \) and \( \angle GJI \) are equal (alternate interior angles). \( \angle GJI \) is supplementary to \( 73^\circ \)? No, \( \angle HJD = 73^\circ \), so \( \angle GJI = 180 - 73 = 107 \)? No, that can't be. Wait, no, \( \angle HJD \) and \( \angle GJI \) are vertical angles? No, \( \angle HJD \) and \( \angle GJC \) are vertical? Wait, maybe I made a mistake in angle relationship. Wait, let's look at the diagram again: \( EF \) is horizontal, \( GH \) is horizontal, \( CD \) is a transversal. So \( \angle EIC \) is on the top left of \( I \), and \( \angle HJD \) is on the bottom right of \( J \). So they are corresponding angles, so they should be equal. So \( 7x - 4 = 73 \), then \( 7x = 77 \), \( x = 11 \). Wait, but let's check: if \( x = 11 \), then \( 7x - 4 = 77 - 4 = 73 \), which matches \( \angle HJD = 73^\circ \). So that works. So the angle \( (7x - 4)^\circ \) is equal to \( 73^\circ \) because they are corresponding angles (since \( EF \parallel GH \) and \( CD \) is transversal). So we set up the equation \( 7x - 4 = 73 \).

Step1: Set up equation from parallel lines

Since \( EF \parallel GH \) and \( CD \) is a transversal, \( \angle EIC = \angle HJD \) (corresponding angles). So:
\( 7x - 4 = 73 \)

Step2: Solve for x

Add 4 to both sides:
\( 7x = 73 + 4 \)
\( 7x = 77 \)

Divide both sides by 7:
\( x = \frac{77}{7} \)
\( x = 11 \)

Answer:

\( 11 \)