Question

what is the value of r? 40.2° r 40.4°

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point is \(360^{\circ}\). But here, we can also note that the angles are part of a set of angles that sum up to \(180^{\circ}\) (since they are adjacent and form a linear - like relationship in the context of the figure).

Step2: Set up the equation

We know that \(r + 40.2^{\circ}+40.4^{\circ}=90^{\circ}\) (assuming the angles are part of a right - angle or a half - circle split in a particular way. If we consider the symmetry and the fact that the sum of non - overlapping angles at a point: in the absence of more complex angle - relationships (like vertical angles etc., but if we assume a simple three - angle sum to \(90^{\circ}\) as a common geometric setup).

$$r=90^{\circ}-(40.2^{\circ} + 40.4^{\circ})$$

Step3: Calculate the value of \(r\)

First, calculate \(40.2^{\circ}+40.4^{\circ}=80.6^{\circ}\). Then \(r = 90^{\circ}-80.6^{\circ}\)

$$r = 9.4^{\circ}$$

Answer:

\(9.4\)