Question

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Explanation:

Step1: Find the adjacent supplementary angle

The adjacent supplementary angle of \(156^{\circ}\) is \(180^{\circ}- 156^{\circ}=24^{\circ}\).

Step2: Use the property of vertical - angle and triangle interior angles sum

Since vertical angles are equal, and the sum of interior angles of a triangle is \(180^{\circ}\). Let the unknown angle be \(x\).
We have \(x + 24^{\circ}=20^{\circ}+35^{\circ}\) (because of the relationship between angles in the two - triangle structure with vertical angles).
Then \(x=20^{\circ}+35^{\circ}-24^{\circ}\).

Step3: Calculate the value of the unknown angle

\(x = 31^{\circ}\).

Answer:

\(31^{\circ}\)