Question

find fg and m∠g.
fg =
m∠g = 60 °

Explanation:

Step1: Identify parallelogram properties

In parallelogram \(GFEH\), opposite sides are equal: \(FG = HE\).

Step2: Get length of FG

Given \(HE = 8\), so \(FG = 8\).

Step3: Use parallelogram angle properties

In a parallelogram, opposite angles are equal, and consecutive angles are supplementary. \(\angle E\) and \(\angle G\) are consecutive angles, so \(m\angle G = 180^\circ - m\angle E\).

Step4: Calculate \(m\angle G\)

Substitute \(m\angle E = 60^\circ\): \(m\angle G = 180^\circ - 60^\circ = 120^\circ\).

Answer:

\(FG = 8\)
\(m\angle G = 120^\circ\)