https://file.aiquickdraw.com/mathbot/file/1725536056103af7evthc.jpg

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.

Determine the value of the missing angle x in a quadrilateral where three angles are 84°, 100°, and 121°.

Learn how to find the missing angle in a quadrilateral with given angles of 84°, 100°, and 121°. This problem involves geometric concepts and the angle sum property. Suitable for students in Grades 6-8.

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