Answer:
The value of x is 108°
Step-by-step explanation:
Given interior angles of parallelogram are:
[tex]\frac{2}{3}x, x, \frac{2}{3}x\ and x[/tex]
The sum of interior angles of a parallelogram is 360°.
We will use this information to find the value of x.
So adding up all the angles and putting the sum equal to 360 we get,
[tex]x+\frac{2}{3}x+x+\frac{2}{3}x = 360[/tex]
[tex]2x+\frac{2}{3}x+\frac{2}{3}x = 360\\2x + \frac{4}{3}x = 360[/tex]
Taking LCM on left side of the equation, as it involves fraction
[tex]\frac{6x+4x}{3} = 360\\\frac{10x}{3} = 360[/tex]
Multiplying both sides by 3
[tex]\frac{10x}{3} * 3 = 360 * 3\\10x = 1080[/tex]
Dividing both sides by 10
[tex]\frac{10x}{10} = \frac{1080}{10}\\x = 108[/tex]
Hence,
The value of x is 108°
