Question

what is the value of j?

Explanation:

Step1: Identify angle - relationship

The large angle is composed of two smaller angles. We know the measures of two of the angles and want to find the third.

Step2: Use angle - addition formula

Let the large angle be composed of angles \(41^{\circ}\), \(j\), and \(67^{\circ}\). The sum of these angles forms a larger angle. If we assume the larger angle is a non - overlapping combination of these three angles, and we know that the sum of the measures of non - overlapping adjacent angles is equal to the measure of the larger angle formed by them. Let's assume the larger angle is a whole and we can write the equation \(41 + j+67 = \text{total angle}\). If we assume the total angle is not given and we are working in a context where these are the only angles being considered in a single angular region, we can use the fact that the sum of the two known angles and the unknown angle \(j\) is related by the equation \(j= \text{total angle}-(41 + 67)\). In the absence of information about the total angle, if we assume these are the only angles in a simple angular composition, we can use the fact that the sum of the two given non - overlapping adjacent angles and \(j\) is such that \(j=67 - 41\).

$$j = 67-41$$

Step3: Calculate the value of \(j\)

$$j=26^{\circ}$$

Answer:

\(26^{\circ}\)