Answer:
See below.
Step-by-step explanation:
Question 1
Statement: Angle B = 60°
Reason: ΔABE is equilateral.
Statement: Angle C = 120°
Reason: ABCD is a parallelogram and adjacent angles in a parallelogram sum to 180°.
⇒ B + C = 180°
⇒ 60° + C = 180°
⇒ C = 120°
Statement: Angle D₂ = Angle E₃ = x
Reason: ΔDEC is an isosceles triangle and E₃ = x.
Statement: x = 30°
Reason: Interior angles in triangle sum to 180°.
⇒ D₂ + E₃ + C = 180°
⇒ x + x + 120° = 180°
⇒ 2x + 120° = 180°
⇒ 2x = 60°
⇒ x = 30°
Statement: E₂ = 90°
Reason: Angles on a straight line sum to 180°
⇒ E₁ + E₂ + E₃ = 180°
⇒ 60° + E₂ + 30° = 180°
⇒ E₂ + 90° = 180°
⇒ E₂ = 90°
Statement: AE ⊥ ED.
Reason: E₂ = 90°
Question 2
Statement: Angle B = 60°
Reason: ΔABE is equilateral.
Statement: Angle C = 120°
Reason: ABCD is a parallelogram and adjacent angles in a parallelogram sum to 180°.
⇒ B + C = 180°
⇒ 60° + C = 180°
⇒ C = 120°
Statement: Angle D₂ = Angle E₃ = x
Reason: ΔDEC is an isosceles triangle and E₃ = x.
Statement: x = 30°
Reason: Interior angles in triangle sum to 180°.
⇒ D₂ + E₃ + C = 180°
⇒ x + x + C120° = 180°
⇒ 2x + 120° = 180°
⇒ 2x = 60°
⇒ x = 30°
Statement: Angle B = Angle D = 60°
Reason: ABCD is a parallelogram and opposite angles in a parallelogram are equal.
Statement: Angle D₁ = 30°
Reason: Angle D is 60° and Angle D₂ is 30°.
⇒ D₁ + D₂ = 60°
⇒ D₁ + 30° = 60°
⇒ D₁ = 30°
Statement: ED bisects angle D
Reason: Angle D₁ = Angle D₂
