Question

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Explanation:

Step1: Recall the property of inscribed angles subtended by the same arc

Angles subtended by the same arc at the circumference of a circle are equal. Also, the angle in a semicircle is \(90^{\circ}\).

Step2: Use the property of right - angled triangle

Since \(GF\) is a diameter (implied by the center - like dot on \(GF\)), \(\angle GPF = 90^{\circ}\) (angle in a semicircle). In \(\triangle GPF\), we know that the sum of angles in a triangle is \(180^{\circ}\). Let the unknown angle be \(x\). Then \(x+56^{\circ}+90^{\circ}=180^{\circ}\).

Step3: Solve for the unknown angle

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Answer:

\(34^{\circ}\)