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The problem asks to find the value of \(x\) given two angles in an angle diagram.

We are provided with two angles:
- One angle is \(2x^\circ\),
- The other angle is \((3x + 5)^\circ\).

From the diagram, we see that the two angles form a linear pair at point \(G\) (a right-angle intersection), which means they add up to 90° (since it forms a right angle at \(G\)).

Thus, we can set up the equation:
\[
2x + (3x + 5) = 90^\circ
\]

Let's solve this:

\[
2x + 3x + 5 = 90
\]
\[
5x + 5 = 90
\]
\[
5x = 90 - 5
\]
\[
5x = 85
\]
\[
x = \frac{85}{5} = 17
\]

So, \(x = 17\).

Would you like further clarification or details?

Here are five related questions to extend your understanding:
1. What is the sum of angles on a straight line?
2. How would you solve if the angles formed a complete circle around point \(G\)?
3. What is the formula for complementary and supplementary angles?
4. Can two angles form a linear pair without being adjacent?
5. How do vertical angles relate to each other?

**Tip:** When angles form a straight line, their sum will always be 180°.

Find the value of x where the angles are (2x)° and (3x + 5)°, forming a linear pair.

Find the value of x in a linear pair problem where angles are given as 2x° and (3x + 5)°. This geometry problem covers angle relationships and algebraic solving methods, suitable for students in Grades 6-8.

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