Question

if ( fg = fi = 62 ), ( mangle fhg = a + 24^{circ} ), and ( mangle fhi = 4a ), what is the value of ( a )?

Explanation:

Step1: Apply the Angle Bisector Theorem

Since \(FG = FI\) and \(FH\) is the common side, \(FH\) bisects \(\angle GHI\). So \(m\angle FHG=m\angle FHI\).

Step2: Set up the equation

We have \(a + 24=4a\).

Step3: Solve the equation

Subtract \(a\) from both sides: \(24=4a - a\), which simplifies to \(24 = 3a\). Then divide both sides by \(3\): \(a=\frac{24}{3}\).

Answer:

\(8\)