Question

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Explanation:

Step1: Find the adjacent angle of \(145^{\circ}\)

Adjacent angles on a straight line sum to \(180^{\circ}\). Let the adjacent angle be \(x\).
\(x + 145^{\circ}=180^{\circ}\)
\(x=180^{\circ}- 145^{\circ}=35^{\circ}\)

Step2: Use the triangle angle - sum property

In the right - angled triangle (where one angle is \(90^{\circ}\), the other non - right angle is \(x = 35^{\circ}\)), and let \(\angle1=y\).
By the triangle angle - sum property (\(90^{\circ}+x + y=180^{\circ}\))
Substitute \(x = 35^{\circ}\) into the equation: \(90^{\circ}+35^{\circ}+y=180^{\circ}\)
\(y=180^{\circ}-(90^{\circ}+35^{\circ})\)
\(y = 55^{\circ}\)

Answer:

\(55\)