Let's solve the problem by analyzing the given diagram.

Problem Analysis:

• We are given two angles:
  • $110^\circ$ (exterior angle on the left side),
  • $130^\circ$ (exterior angle on the right side).
• We need to find the value of $x$, which is an interior angle of the triangle.

Solution:

Step 1: Calculate the third exterior angle

The sum of the exterior angles on a straight line is $180^\circ$. This gives: 180^\circ - 110^\circ = 70^\circ \quad \text{(Angle adjacent to 110^\circ)}.

Step 2: Sum of angles in a triangle

The sum of all interior angles of a triangle is always $180^\circ$. So, we have: $x + 70^\circ + 50^\circ = 180^\circ,$ where $50^\circ$ is the interior angle adjacent to $130^\circ$ (since $180^\circ - 130^\circ = 50^\circ$).

Step 3: Solve for $x$

$x = 180^\circ - (70^\circ + 50^\circ),$ $x = 180^\circ - 120^\circ = 60^\circ.$

Final Answer:

$\boxed{x = 60^\circ}$

Would you like a more detailed breakdown of any step? Let me know!

Related Questions:

1. What are exterior and interior angles in a triangle?
2. How does the sum of angles in a triangle relate to exterior angles?
3. Can a triangle have more than one obtuse angle? Why or why not?
4. What is the property of angles on a straight line?
5. How can you verify the solution using a different method?

Tip:

Always check if the angles in your solution satisfy the sum of $180^\circ$ for the triangle to ensure accuracy!