https://file.aiquickdraw.com/mathbot/file/1725922009658gdf5pu8k.jpg

The problem in the image involves finding the value of \( x \) and determining the measures of each labeled angle in a quadrilateral. Let's break it down:

### Step 1: Identifying the angles
- One of the angles is labeled \( x^\circ \).
- Another angle is labeled \( (x - 30)^\circ \).
- There is a right angle, which measures \( 90^\circ \).
- The fourth angle is also unknown, but we will use the fact that the sum of all interior angles in a quadrilateral equals \( 360^\circ \).

### Step 2: Applying the sum of interior angles
The sum of the four angles in any quadrilateral is \( 360^\circ \). Therefore, we can write the equation:
\[
x + (x - 30) + 90 + 90 = 360
\]
Simplify the equation:
\[
x + (x - 30) + 180 = 360
\]
\[
2x - 30 + 180 = 360
\]
\[
2x + 150 = 360
\]
\[
2x = 360 - 150
\]
\[
2x = 210
\]
\[
x = 105
\]

### Step 3: Finding the measures of each angle
Now that we know \( x = 105^\circ \), we can find the other angles:
- The first angle is \( x = 105^\circ \).
- The second angle is \( x - 30 = 105^\circ - 30^\circ = 75^\circ \).
- The third and fourth angles are both \( 90^\circ \) (right angles).

So, the angles are:
- \( 105^\circ \)
- \( 75^\circ \)
- \( 90^\circ \)
- \( 90^\circ \)

Would you like further details on how this applies or have any other questions?

### Relative questions:
1. What is the sum of interior angles in a quadrilateral?
2. How do you solve for an unknown angle when given multiple angles in a figure?
3. What are the properties of a right angle?
4. Can the same approach be used for triangles? How would it differ?
5. How does knowing the properties of a quadrilateral help in solving geometry problems?

### Tip:
Always remember that the sum of the interior angles of any quadrilateral is \( 360^\circ \), which is key in solving for unknown angles.

Find the value of x. Then find the measure of each labeled angle in a quadrilateral, where one angle is x, another is (x - 30), and there is a right angle (90°).

Learn how to solve for x in a quadrilateral using the properties of interior angles. This problem demonstrates how the sum of angles in a quadrilateral equals 360° and includes the use of basic algebra.

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