Question

Find the measure of each angle of a parallelogram, if one of its adjacent angle is 30° less than twice

the smallest angle​

Answer 1

Step-by-step explanation:

Find the measure of each angle of a parallelogram, if one of its adjacent angle is 30° less than twice

Answer 2

Given :

• One of its adjacent angle is 30° less than twice the smallest angle.

To Find :

• The measure of each angle of the Parallelogram.

Solution :

✰ As we know that, Sum of two adjacent angles of a Parallelogram are equal to 180°, this means 1st angle + 2nd angle = 180° , now it is given that One of its adjacent angle is 30° less than twice the smallest angle therefore :

⟾ Let the smallest angle be x

⟾ Then other angle will be 2x - 30°

⠀⠀⠀

According to the Question :

⠀⠀⟼⠀⠀1st angle + 2nd angle = 180°

⠀⠀⟼⠀⠀(x) + (2x - 30°) = 180°

⠀⠀⟼⠀⠀x + 2x - 30° = 180°

⠀⠀⟼⠀⠀x + 2x = 180° + 30°

⠀⠀⟼⠀⠀x + 2x = 210°

⠀⠀⟼⠀⠀3x = 210

⠀⠀⟼⠀⠀x = 210 / 3

⠀⠀⟼⠀⠀x = 70°

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Verification :

⠀⠀➟⠀⠀1st angle + 2nd angle = 180°

⠀⠀➟⠀⠀(x) + (2x - 30°) = 180°

⠀⠀➟⠀⠀(70°) + (2{70°} - 30°) = 180°

⠀⠀➟⠀⠀70° + (140° - 30°) = 180°

⠀⠀➟⠀⠀70° + 110° = 180°

⠀⠀➟⠀⠀180° = 180°

Hence Verified

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Therefore :

⠀⠀⟿⠀⠀First Angle = x

⠀⠀⟿⠀⠀First Angle = 70°

⠀

⠀⠀⟿⠀⠀Second Angle = 2x - 30°

⠀⠀⟿⠀⠀Second Angle = 2(70) - 30°

⠀⠀⟿⠀⠀Second Angle = 140° - 30°

⠀⠀⟿⠀⠀Second Angle = 110°

Thus Angle of the Parallelogram are 70°, 110° , 70° , 110°.

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Tips and Tricks :

Tips and tricks to solve a word problem.

1. Read the problem carefully and note what is given what is required.
2. Denote the unknown quantity by some letters, say x,y,z etc.
3. Translate the statement of the problem into mathematical statements.
4. Using the condition (s) given in the problem, form the equation.
5. Solve the equation for the unknown.
6. Check whether the solution satisfies the equation

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