10. find the value of x.

Explanation:

Step1: Recall polygon - angle sum formula

The sum of interior angles of an (n) - sided polygon is given by ((n - 2)\times180^{\circ}). For a pentagon ((n = 5)), the sum of interior angles is ((5 - 2)\times180^{\circ}=540^{\circ}).

Step2: Set up an equation

The interior angles of the pentagon are (x^{\circ},x^{\circ},2x^{\circ},120^{\circ},120^{\circ}). So, (x + x+2x + 120+120=540).

Step3: Combine like - terms

Combining the (x) terms and the constant terms, we get (4x+240 = 540).

Step4: Solve for (x)

Subtract 240 from both sides: (4x=540 - 240), so (4x = 300). Then divide both sides by 4: (x=\frac{300}{4}=75).

Answer:

(x = 75)