https://file.aiquickdraw.com/mathbot/file/1729207923680zebohpsn.jpg

To solve for \(x\) in the given figure, we can use the properties of angles and triangles.

### Step 1: Analyzing the figure
- We observe that one of the angles in the triangle is a right angle (90°).
- There is a 30° angle at the top and a 40° angle at the bottom right.

### Step 2: Using the exterior angle theorem
The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. Here, \(x\) is an exterior angle, opposite to the 30° and 40° angles.

Thus,
\[
x = 30^\circ + 40^\circ = 70^\circ
\]

So, the value of \(x\) is \(70^\circ\).

Would you like a detailed explanation, or do you have any questions?

### Related Questions:
1. What is the exterior angle theorem and how is it applied in other scenarios?
2. How do different types of triangles (isosceles, equilateral) affect angle properties?
3. What are the properties of supplementary and complementary angles?
4. How can we solve for unknown angles in polygons with more than three sides?
5. How does the sum of interior angles change with the number of sides in a polygon?

### Tip:
Remember that in any triangle, the sum of the interior angles is always \(180^\circ\). This property can help in solving various angle-related problems.

In the figure shown, what is the value of x?

Learn how to solve for x in a triangle using the exterior angle theorem. This geometry problem involves finding the unknown angle in a triangle, utilizing key geometric concepts such as the sum of interior angles and exterior angles. Suitable for students in Grades 7-10.

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