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°.