Question

what is m∠ghi?

m∠ghi = \boxed{}^circ
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Explanation:

Step1: Use the Angle Bisector Theorem

Since the segments from \(F\) to the sides \(GH\) and \(HI\) are equal (marked with the same tick), \(F\) is on the angle bisector of \(\angle GHI\). So, \(2p + 51=12p-99\).

Step2: Solve for \(p\)

Subtract \(2p\) from both sides: \(51 = 10p-99\).
Add \(99\) to both sides: \(51 + 99=10p\), so \(150 = 10p\).
Divide both sides by \(10\): \(p = 15\).

Step3: Calculate \(\angle GHI\)

\(\angle GHI=(2p + 51)+(12p-99)\).
Substitute \(p = 15\): \((2\times15 + 51)+(12\times15-99)=(30 + 51)+(180-99)=81 + 81=162\).

Answer:

\(162\)