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
