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

Sagot :

MrRoyal

Answer:

Square

Step-by-step explanation:

Given

[tex]\angle 1 = x + 60[/tex]

[tex]\angle 2 = 2x + 30[/tex]

1 and 2 are consecutive

Required

Determine a special name to the parallelogram

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

[tex]\angle 1 + \angle 2 = 180[/tex]

[tex]x + 60 + 2x + 30 = 180[/tex]

[tex]3x +90 = 180[/tex]

Collect like terms

[tex]3x = 180 - 90[/tex]

[tex]3x = 90[/tex]

[tex]x = 30[/tex]

Next, is to calculate angles 1 and 2

[tex]\angle 1 = x + 60[/tex]

[tex]\angle = 30 + 60 = 90[/tex]

[tex]\angle 2 = 2x + 30[/tex]

[tex]\angle 2= 2*30 + 30 = 90[/tex]

Both angles are 90.

This implies that each angle in the parallelogram is 90.

Such a parallelogram is either a rectangle or a square

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