Question

find the measure of $\angle bhe$.
$m\angle bhe = \square^\circ$

Explanation:

Step1: Identify parallel lines and equal angles

Since \( DE \parallel FG \) (from the diagram, they are parallel lines cut by a transversal), \( \angle BHE \) and \( \angle BIG \) (wait, actually \( \angle BHE \) and \( \angle BIF \)? No, more accurately, \( \angle BHE \) and \( \angle BIG \) are corresponding angles? Wait, no, the angles \( (55 - 2x)^\circ \) and \( (64 - 5x)^\circ \) are corresponding angles, so they should be equal. So set \( 55 - 2x = 64 - 5x \).

Step2: Solve for \( x \)

\( 55 - 2x = 64 - 5x \)
Add \( 5x \) to both sides: \( 55 + 3x = 64 \)
Subtract 55 from both sides: \( 3x = 9 \)
Divide by 3: \( x = 3 \)

Step3: Find \( m\angle BHE \)

Substitute \( x = 3 \) into \( 55 - 2x \):
\( 55 - 2(3) = 55 - 6 = 49 \)

Answer:

\( 49 \)