Question

what is the value of k?

\t

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal.

Step2: Determine the value of \(k\)

Since \(k\) and \(79.6^{\circ}\) are vertical angles, \(k = 180^{\circ}- 79.6^{\circ}\) is incorrect. Wait, no! Wait, actually, when two lines intersect, vertical angles are equal. So \(k = 180^{\circ}-(180^{\circ}-79.6^{\circ})\) simplifies to \(k = 79.6^{\circ}\) (no, wait, another approach: when two lines intersect, the sum of adjacent angles is \(180^{\circ}\). But vertical angles (opposite angles) are equal. So \(k\) and \(79.6^{\circ}\) are vertical angles. So \(k=100.4^{\circ}\) is wrong. Wait, no! Wait, adjacent angles on a straight - line sum to \(180^{\circ}\). Let's re - do.

Let's use the linear - pair property first. Let the adjacent angle to \(79.6^{\circ}\) be \(x\), then \(x + 79.6^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-79.6^{\circ}=100.4^{\circ}\). But \(k\) and \(x\) are adjacent angles forming a linear pair? No, no! Wait, \(k\) and \(79.6^{\circ}\) are adjacent angles forming a linear pair. So \(k+79.6^{\circ}=180^{\circ}\)

Step3: Solve for \(k\)

$$
LATEXBLOCK0
$$

Answer:

\(100.4\)