Question

Which statements regarding the diagram are true?
Check all that apply.
XFG is an interior angle of AEFG.
EFG is an interior angle of AEFG.
FEZ is an exterior angle of AEG.
YGE is an exterior angle of AEFG.
LEGF and angle FGY are supplementary angles.
FEG and FGE are supplementary angles.

Answer 1

Answer:

EFG is an interior angle of  triangle EFG

FEZ is an exterior angle of  triangle EFG

Angle EGF and angle FGY are supplementary angles

Step-by-step explanation:

we know that

In the triangle EFG of the figure

The interior angles of AEFG are

m∠EFG

m∠FEG

m∠FGE

The exterior angles of AEFG are

m∠XFG

m∠FEZ

m∠FGY

Verify each statement

case a) XFG is an interior angle of  triangle EFG

The statement is false

Because m∠XFG is an exterior angle

case b) EFG is an interior angle of  triangle EFG

The statement is true

case c) FEZ is an exterior angle of  triangle EFG

The statement is true

case d) YGE is an exterior angle of  triangle EFG

The statement is false

The measure of m∠YGE=180°

case e) Angle EGF and angle FGY are supplementary angles

The statement is true

Because, their sum is equal to 180 degrees (form a linear pair)

m∠FEG+m∠FGY=180°

case f) FEG and FGE are supplementary angles

The statement is false

Because

m∠FEG+m∠FGE<180°

Remember that the sum of the three interior angles of a triangle must be equal to 180 degrees , not the sum of two interior angles.

Answer 2

The only true statements about the triangle and angles given are;

Option B; ∠EFG is an interior angle of ΔEFG

Option C; ∠FEZ is an exterior angle of  ΔEFG

Option E; ∠EGF and ∠FGY are supplementary angles

Let us analyze each of the given options;

Option A; ∠XFG is an interior angle of ΔEFG

This statement is not true because ∠XFG is an exterior angle of ΔEFG.

Option B; ∠EFG is an interior angle of ΔEFG;

This statement is true because we can see that in the given image, that ∠EFG lies inside ΔEFG.

Option C; ∠FEZ is an exterior angle of  ΔEFG

This statement is true because we can see that ∠FEZ lies outside of ΔEFG

Option D; ∠YGE is an exterior angle of ΔEFG

This statement is not true because ∠YGE is a straight line which means it measures an angle of 180°

Option E; ∠EGF and ∠FGY are supplementary angles

This statement is true because they are angles that form a straight line and their sum must be 180°. Supplementary angles sum up to  180°.

Option F; ∠FEG and ∠FGE are supplementary angles

This statement is false because they are just two of the interior angles inside ΔEFG and as such they cannot sum up to  180° and are therefore not supplementary.

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