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To find the measure of the fourth angle in a quadrilateral, we need to use the fact that the sum of all angles in a quadrilateral is always \(360^\circ\).

Given angles are: \(45^\circ\), \(90^\circ\), and \(120^\circ\).

Let's calculate the measure of the fourth angle:

\[
\text{Sum of given angles} = 45^\circ + 90^\circ + 120^\circ = 255^\circ
\]

Now, subtract this sum from \(360^\circ\) to find the fourth angle:

\[
\text{Fourth angle} = 360^\circ - 255^\circ = 105^\circ
\]

So, the measure of the fourth angle is:

**105°**

Would you like to see further details or have any questions?

Here are 5 related questions you might explore:

1. What is the sum of the angles in a pentagon?
2. How do you find missing angles in polygons?
3. What is the difference between internal and external angles of polygons?
4. How does the sum of angles change as the number of sides of a polygon increases?
5. What is the formula for the sum of interior angles of an \(n\)-sided polygon?

**Tip:** Remember, the sum of the interior angles of a polygon with \(n\) sides is given by \((n-2) \times 180^\circ\).

If three of the angles in a quadrilateral measure 45°, 90°, and 120°, what is the measure of the fourth angle?

Learn how to find the missing angle in a quadrilateral when three angles are provided. The problem involves using the sum of interior angles theorem and basic geometric concepts. Suitable for students in Grades 6-8.

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