Question

Find the measure of all the angles of a parallelogram, if one angle is 24° less than twice the smallest angle.

Answer 1

Given :  One angle of a parallelogram is 24° less than twice the smallest angle.

Let the smallest angle of a parallelogram = x°  

The other angle of a parallelogram = (2x - 24)°

We know that ,the sum of the 4 angles of a parallelogram is 360°.

x° + x° + 2x - 24 + 2x - 24 = 360°

[Opposite angles of a parallelogram are equal]

2x° + 4x° - 48 = 360°

6x° = 360° + 48°

6x° = 408

x = 408/6

x = 68°

Smallest angle of a parallelogram = x° = 68°  

other angle of a parallelogram = (2x - 24)° = (2 × 68 - 24) = 136° - 24° = 112°

Hence, four angles are 68°, 112°, 68°, 112°

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Answer 2

Answer:-

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Given :

 One angle of a parallelogram is 24° less than twice the smallest angle.

Let the smallest angle of a parallelogram = x°  

The other angle of a parallelogram = (2x - 24)°

We know that ,the sum of the 4 angles of a parallelogram is 360°.

x° + x° + 2x - 24 + 2x - 24 = 360°

[Opposite angles of a parallelogram are equal]

2x° + 4x° - 48 = 360°

6x° = 360° + 48°

6x° = 408

x = 408/6

x = 68°

Smallest angle of a parallelogram = x° = 68°  

other angle of a parallelogram = (2x - 24)° = (2 × 68 - 24) = 136° - 24° = 112°

Hence, four angles are 68°, 112°, 68°, 112°

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