Question

which statements regarding the diagram are true? check all that apply. ∠xfg is an interior angle of △efg. ∠efg is an interior angle of △efg. ∠fez is an exterior angle of △efg. ∠yge is an exterior angle of △efg. ∠egf and ∠fgy are supplementary angles. ∠feg and ∠fge are supplementary angles.

Explanation:

Step1: Recall interior - angle definition

An interior angle of a triangle is an angle formed by two sides of the triangle. In \(\triangle EFG\), \(\angle EFG\) is formed by sides \(EF\) and \(FG\), so \(\angle EFG\) is an interior angle of \(\triangle EFG\). \(\angle XFG\) is not an interior angle of \(\triangle EFG\) since ray \(FX\) is not a side of \(\triangle EFG\).

Step2: Recall exterior - angle definition

An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side. \(\angle FEZ\) is formed by side \(EF\) and the extension of side \(EG\) (in the direction of \(EZ\)), so \(\angle FEZ\) is an exterior angle of \(\triangle EFG\). \(\angle YGE\) is formed by side \(EG\) and the extension of side \(FG\) (in the direction of \(GY\)), so \(\angle YGE\) is an exterior angle of \(\triangle EFG\).

Step3: Recall supplementary - angle definition

Two angles are supplementary if their sum is \(180^{\circ}\). \(\angle EGF\) and \(\angle FGY\) form a linear - pair (a straight - line angle), so \(\angle EGF+\angle FGY = 180^{\circ}\), and they are supplementary. \(\angle FEG\) and \(\angle FGE\) are two interior angles of \(\triangle EFG\), and their sum is not \(180^{\circ}\) (the sum of the three interior angles of \(\triangle EFG\) is \(180^{\circ}\)), so they are not supplementary.

Answer:

• \(\angle EFG\) is an interior angle of \(\triangle EFG\).
• \(\angle FEZ\) is an exterior angle of \(\triangle EFG\).
• \(\angle YGE\) is an exterior angle of \(\triangle EFG\).
• \(\angle EGF\) and \(\angle FGY\) are supplementary angles.