Question

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Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of the interior angles of a quadrilateral is $(4 - 2)\times180^{\circ}=360^{\circ}$.

Step2: Set up an equation

We know the angles of the quadrilateral are $35^{\circ}$, $x^{\circ}$, $127^{\circ}$, and $65^{\circ}$. So the equation is $35 + x+127 + 65=360$.

Step3: Simplify the left - hand side of the equation

$35+127 + 65+x=(35 + 127+65)+x=227+x$.

Step4: Solve for $x$

We have the equation $227+x = 360$. Subtract 227 from both sides: $x=360 - 227$.
$x = 133$.

Answer:

$133$