Question

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Answer 1

Answer:

The value of x is 108°

Step-by-step explanation:

Given interior angles of parallelogram are:

$\frac{2}{3}x, x, \frac{2}{3}x\ and x$

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,

$x+\frac{2}{3}x+x+\frac{2}{3}x = 360$

$2x+\frac{2}{3}x+\frac{2}{3}x = 360\\2x + \frac{4}{3}x = 360$

Taking LCM on left side of the equation, as it involves fraction

$\frac{6x+4x}{3} = 360\\\frac{10x}{3} = 360$

Multiplying both sides by 3

$\frac{10x}{3} * 3 = 360 * 3\\10x = 1080$

Dividing both sides by 10

$\frac{10x}{10} = \frac{1080}{10}\\x = 108$

Hence,

The value of x is 108°