Ingles \( A \) and \( B \) are corresponding angles formed by two parallel lines cut by a transversal. If \( n \angle A=4 x \) and \( m \angle B=3 x+7 \), find the value of \( x \). Explain. \[ 4 x=3 x+7 \] ingles \( G \) and \( H \) are supplementary and congruent. If \( \angle G \) and \( \angle H \) are alternate interior angle

To solve for \( x \) using the equation \( 4x = 3x + 7 \), start by isolating \( x \). Subtract \( 3x \) from both sides to get: \[ 4x - 3x = 7 \] This simplifies to: \[ x = 7 \] Now that we have \( x \), we can find the measures of angles \( A \) and \( B \). Substituting \( 7 \) back into \( n \angle A = 4x \) gives: \[ n \angle A = 4(7) = 28^\circ \] And for \( m \angle B \): \[ m \angle B = 3(7) + 7 = 21 + 7 = 28^\circ \] Thus, both angles \( A \) and \( B \) are \( 28^\circ \), confirming they are indeed congruent as corresponding angles! When angles \( G \) and \( H \) are supplementary and congruent, each angle measures \( 90^\circ \). So if \( G + H = 180^\circ \) and \( G = H \), you would set it up as \( 2G = 180^\circ \). Solving for \( G \) gives \( G = H = 90^\circ \), which means they are both right angles, perfect for your alternate interior angles scenario!