Question

what is the value of t?

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\). But here we have two right - angles (since the lines are perpendicular in pairs, and we can consider the sum of the three given angles and \(t\) in a quarter - circle or use the fact that the sum of angles in a set of intersecting lines where we can group them. Another approach is to use the fact that the sum of angles in a 'cross' - like figure (two perpendicular lines) gives us that the sum of the three given angles and \(t\) is \(180^{\circ}\) (because we can consider a straight - line pair of angles).
We know that \(47.5^{\circ}+82.2^{\circ}+t = 90^{\circ}\) (using the property of complementary angles in a right - angle formed by the perpendicular lines).

Step2: Solve for \(t\)

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$$

Answer:

\(40.3\)