Question

31° x = 105 106° x°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let the third - interior angle of the triangle be \(y\). So, \(y+31^{\circ}+106^{\circ}=180^{\circ}\).

Step2: Calculate the third - interior angle \(y\)

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Step3: Use the linear - pair property

The angle \(x\) and the interior angle \(y\) form a linear pair. A linear pair of angles sums to 180°. So, \(x + y=180^{\circ}\).

Step4: Calculate the value of \(x\)

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Answer:

\(x = 137\)