Question

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Explanation:

Step1: Identify isosceles - triangle property

Since $PR = PQ$ (indicated by the equal - side marks), $\angle R=\angle Q = 2x^{\circ}$.

Step2: Apply angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $\angle P+\angle Q+\angle R = 180^{\circ}$. Substitute $\angle P = 40^{\circ}$, $\angle Q = 2x^{\circ}$, and $\angle R = 2x^{\circ}$ into the equation: $40 + 2x+2x=180$.

Step3: Simplify the equation

Combine like terms: $40 + 4x=180$.

Step4: Solve for $x$

Subtract 40 from both sides: $4x=180 - 40=140$. Then divide both sides by 4: $x=\frac{140}{4}=35$.

Answer:

$x = 35$