Question

if ( mangle fhc = 73^{circ} ), then what is ( mangle fhd )?

Explanation:

Step1: Vertical angles

Since \( \angle FHC\) and \( \angle 4\) are vertical angles, \(m\angle4 = m\angle FHC=73^{\circ}\).

Step2: Linear - pair relationship

\(\angle4\) and \(\angle FHD\) form a linear pair. By the linear - pair postulate, \(m\angle4 + m\angle FHD=180^{\circ}\).
Substitute \(m\angle4 = 73^{\circ}\) into the equation: \(73^{\circ}+m\angle FHD = 180^{\circ}\).

Step3: Solve for \(m\angle FHD\)

\(m\angle FHD=180^{\circ}-73^{\circ}\).

Answer:

\(107\)