Question

Which statements are true

Answer 1

Answer: 1. False.

2.True.

3.True.

4.False.

5.True.

6.False.

Explanation:

1.∠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.∠EFG is lying between the two sides of the ΔEFG, therefore it is an interior angle of the triangle.

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

4.∠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.∠EGF and FGY lying on the same line YZ ,∴they are linear pair i.e. they are supplementary angles.

6.∠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.Therefore ∠FEG and ∠FGE are not supplementary angles.

Answer 2

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)