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maths geometry

Please help maths geometry-example-1
User Amudhan
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Answer:

See below.

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

User Jdamae
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