Question

two consecutive angles of a parallelogram are (X + 60 degree)and (2 X + 30) what special name can you give to this parallelogram

Answer 1

A rectangle or a square

Answer 2

Given :

• Two consecutive angles of a parallelogram are (x + 60°) and (2x + 30°).

To Find :

• Angles of the Parallelogram.
• Special name for this parallelogram.

Solution :

✰ As we know that, consecutive interior angles of a Parallelogram are Supplementary. This means, the sum of the two consecutive interior angles will be equal to 180°.

⠀⠀⠀

⠀⠀⟼⠀⠀1st angle + 2nd angle = 180°

⠀⠀⟼⠀⠀(x + 60°) + (2x + 30°) = 180°

⠀⠀⟼⠀⠀x + 2x + 60° + 30° = 180°

⠀⠀⟼⠀⠀3x + 60° + 30° = 180°

⠀⠀⟼⠀⠀3x + 90° = 180°

⠀⠀⟼⠀⠀3x = 180° - 90°

⠀⠀⟼⠀⠀3x = 90°

⠀⠀⟼⠀⠀x = 90° / 3

⠀⠀⟼⠀⠀x = 30°

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Verification :

⠀⠀➟⠀⠀1st angle + 2nd angle = 180°

⠀⠀➟⠀⠀(x + 60°) + (2x + 30°) = 180°

⠀⠀➟⠀⠀(30 + 60°) + (2(30) + 30°) = 180°

⠀⠀➟⠀⠀90° + (60° + 30°) = 180°

⠀⠀➟⠀⠀90° + 90° = 180°

⠀⠀➟⠀⠀180° = 180°

Hence Verified

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Therefore :

⠀⠀⟿⠀⠀First Angle = x + 60°

⠀⠀⟿⠀⠀First Angle = 30° + 60°

⠀⠀⟿⠀⠀First Angle = 90°

⠀

⠀⠀⟿⠀⠀Second Angle = 2x + 30°

⠀⠀⟿⠀⠀Second Angle = 2(30) + 30°

⠀⠀⟿⠀⠀Second Angle = 60° + 30°

⠀⠀⟿⠀⠀Second Angle = 90°

⠀

Hence, the special name of the given parallelogram is Rectangle.

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