Question

Two consecutive angles of a parallelogram are (x + 60)° and (2x + 30)°. What special name can you give to this parallelogram ?

Answer 1

Square

Explanation:

Given

`\angle 1 = x + 60`

`\angle 2 = 2x + 30`

1 and 2 are consecutive

Required

Determine a special name to the parallelogram

For consecutive angles 1 and 2 of a parallelogram, we have:

`\angle 1 + \angle 2 = 180`

`x + 60 + 2x + 30 = 180`

`3x +90 = 180`

Collect like terms

`3x = 180 - 90`

`3x = 90`

`x = 30`

Next, is to calculate angles 1 and 2

`\angle 1 = x + 60`

`\angle = 30 + 60 = 90`

`\angle 2 = 2x + 30`

`\angle 2= 2*30 + 30 = 90`

Both angles are 90.

This implies that each angle in the parallelogram is 90.

Such a parallelogram is either a rectangle or a square