We are given a diagram of a quadrilateral with two sides parallel to each other. The two parallel sides are also of equal length. We are given one exterior angle is $84^{\circ}$ and need to find the value of angle $k$.

1. Problem Description

We are given a diagram of a quadrilateral with two sides parallel to each other. The two parallel sides are also of equal length. We are given one exterior angle is $84^{\circ}$ and need to find the value of angle $k$.

2. Solution Steps

Since the figure has two parallel sides of equal length, it is an isosceles trapezoid. Therefore, the base angles are equal. The angle adjacent to the $84^\circ$ angle is supplementary to it. This angle and $k$ are base angles. The sum of supplementary angles is $180^\circ$, therefore:

$180^\circ = 84^\circ + x$

$x = 180^\circ - 84^\circ = 96^\circ$

So, one of the base angles is $96^\circ$. Since the trapezoid is isosceles, both base angles are equal. So, $k = 96^\circ$.

3. Final Answer

96