Question

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Explanation:

Step1: Calculate the right - angled triangle's unknown angle

In a right - angled triangle, the sum of angles is \(180^{\circ}\).
Let the unknown angle in the right - angled triangle be \(x\).
\(x+90^{\circ}+36^{\circ}=180^{\circ}\)
\(x = 180^{\circ}-90^{\circ}-36^{\circ}=54^{\circ}\)

Step2: Calculate the quadrilateral's unknown angle

The sum of angles in a quadrilateral is \(360^{\circ}\).
Let the unknown angle be \(y\).
\(y + 86^{\circ}+84^{\circ}+54^{\circ}=360^{\circ}\)
\(y=360^{\circ}-86^{\circ}-84^{\circ}-54^{\circ}\)
\(y = 136^{\circ}\)

Answer:

\(136^{\circ}\)