Question

use the diagram to find the missing measures. the measure of angle ghe is □. the length of ̲ge is □.

Explanation:

Step1: Use the property of congruent triangles (SSS)

Since \(EF = GH\), \(EH = HG\), and \(FH = EH\) (marked by the same tick marks), \(\triangle EFH\cong\triangle GHE\) (by SSS - Side - Side - Side congruence criterion).

Step2: Find the measure of \(\angle GHE\)

Because \(\triangle EFH\cong\triangle GHE\), \(\angle GHE=\angle FEH\). Given \(\angle FEH = 62^{\circ}\), so \(\angle GHE=62^{\circ}\).

Step3: Find the length of \(GE\)

Since \(\triangle EFH\cong\triangle GHE\), \(GE = FH\). Given \(FH = 30\), so \(GE = 30\).

Answer:

The measure of angle \(GHE\) is \(62^{\circ}\). The length of \(\overline{GE}\) is \(30\).