Question

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Explanation:

Step1: Find supplementary angles

The supplementary angle of \(115^{\circ}\) is \(180 - 115=65^{\circ}\), and the supplementary angle of \(155^{\circ}\) is \(180 - 155 = 25^{\circ}\).

Step2: Calculate the value of \(x\)

Since the sum of angles around a point is \(360^{\circ}\), and there is a right - angle (\(90^{\circ}\)) in the figure. Let \(x\) be the unknown angle. Then \(x=360-(65 + 90+25 + 90)\). First, calculate \(65 + 90+25 + 90=(65 + 25)+(90 + 90)=90+180 = 270\). So \(x = 360-270=90^{\circ}\).

Answer:

\(90^{\circ}\)