The image shows a quadrilateral with four angles. Three of the angles are given:

• $84^\circ$
• $100^\circ$
• $121^\circ$

The fourth angle is $x^\circ$, and we need to determine its value.

In any quadrilateral, the sum of all interior angles is always $360^\circ$.

Thus, we can use the equation:

$84^\circ + 100^\circ + 121^\circ + x^\circ = 360^\circ$

Let's solve for $x$.

$x^\circ = 360^\circ - (84^\circ + 100^\circ + 121^\circ)$

$x^\circ = 360^\circ - 305^\circ = 55^\circ$

So, $x = 55^\circ$.

Would you like further details on this solution, or do you have any questions?

Here are some related questions for further practice:

1. What is the sum of the interior angles of a pentagon?
2. How do you calculate the exterior angle of a polygon?
3. What is the sum of the exterior angles for any polygon?
4. Can you determine the angles of a trapezoid if you only know three angles?
5. What is the relationship between opposite angles in a cyclic quadrilateral?

Tip: In any polygon, the sum of interior angles can be calculated using the formula $180(n - 2)$, where $n$ is the number of sides.