Question

1. what is the measure of angle egh?

26°
78°
38°
102°

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(EFG\), \(\angle EGH\) is an exterior angle. The two non - adjacent interior angles are \(\angle E = 64^{\circ}\) and \(\angle F=38^{\circ}\).

Step2: Calculate \(\angle EGH\)

By the exterior angle theorem, \(\angle EGH=\angle E+\angle F\). Substitute \(\angle E = 64^{\circ}\) and \(\angle F = 38^{\circ}\) into the formula: \(\angle EGH=64^{\circ}+38^{\circ}\).

$$
LATEXBLOCK0
$$

Answer:

\(102^{\circ}\)