Question

find ( mangle bhf ) if ( mangle abh = 36 ) and ( mangle gfh = 40 ).

Explanation:

Step1: Identify Parallel Lines and Alternate Interior Angles

From the diagram, \( AB \parallel HD \parallel GF \) (since the arrows indicate parallel lines). So, \( \angle ABH \) and \( \angle BHD \) are alternate interior angles, and \( \angle GFH \) and \( \angle FHD \) are alternate interior angles. Thus, \( m\angle BHD = m\angle ABH = 36^\circ \) and \( m\angle FHD = m\angle GFH = 40^\circ \).

Step2: Calculate \( m\angle BHF \)

To find \( m\angle BHF \), we add \( m\angle BHD \) and \( m\angle FHD \) because \( \angle BHF = \angle BHD + \angle FHD \).

$$ m\angle BHF = 36^\circ + 40^\circ = 76^\circ $$

Answer:

B. 76