The image shows a triangle with angles represented algebraically. The angle on the left is given as $5x + 62^\circ$, the angle at the top is $37^\circ$, and the angle on the right is $3x + 47^\circ$.

To write an equation, we use the fact that the sum of the interior angles of any triangle is always $180^\circ$. Thus, we can write the equation:

$(5x + 62) + 37 + (3x + 47) = 180$

Simplifying the equation:

$5x + 62 + 37 + 3x + 47 = 180$

$8x + 146 = 180$

Now, solve for $x$.

Would you like to proceed with the solution or need further explanation?

Here are five related questions:

1. What is the process for solving a simple linear equation like this one?
2. What happens if the sum of the angles in a triangle exceeds $180^\circ$?
3. How can you check your answer for the value of $x$ after solving the equation?
4. What if the angles were given in terms of different variables?
5. What is the relationship between the angles in an isosceles triangle?

Tip: Always double-check the angle sum property in a triangle before solving!