Question

Which statements are true

Answer 1

1) ∠XFG is an interior angle of ΔEFG. - False

(∠XFG is an exterior angle of ΔEFG since that angle is out of the triangle)

2) ∠EFG is an interior angle of ΔEFG. - True

(∠EFG is an interior angle since it is included in the ΔEFG)

3) ∠FEZ is an exterior angle of ΔEFG. - True

(∠FEZ is an exterior angle as it it is out of the triangle EFG)

4) ∠YGE is an exterior angle of ΔEFG. - False

(∠YGE is not an exterior nor an interior angle since it is a straight line)

5) ∠EGF and ∠FGY are supplementary angles. - False

(∠EGF and ∠FGY do not add up to 180° so they are not supplementary)

6) ∠FEG and ∠FGE are supplementary angles. - False

(∠FEG and ∠FGE do not add up to 180° so they are not supplementary)

Answer 2

Answer: 1. False. [∠XFG is lying between the one side and the line extended to the next side of the triangle, therefore it is an exterior angle.]

2.True. [∠EFG is lying between the two sides of the ΔEFG, therefore it is an interior angle of the triangle]

3.True. [∠FEZ is lying between the one side and the line extended to the other side of ΔEFG ]

4.False. [∠YGE is a straight line it is between the one side and the line extended to the same side ∴ it cannot be an exterior angle of the triangle ]

5. True.[∠EGF and FGY together make a straight line therefore they are supplementary angles]

6.False.[∠FEG and ∠FGE are both the interior angles of a triangle and we know that for supplementary angles they should lie on the same line or together make a straight line]