The image contains a triangle with some known and unknown angles. Here's the breakdown of the problem:

1. One triangle is marked with angles $54^\circ$, $60^\circ$, and an unknown angle $y^\circ$.
2. The other triangle adjacent to it shares the angle $y^\circ$, and it has another known angle of $65^\circ$, with the last unknown angle marked as $x^\circ$.

Steps to solve:

1. For the first triangle (with angles $54^\circ$, $60^\circ$, and $y^\circ$): The sum of the angles in any triangle is $180^\circ$. So, $54^\circ + 60^\circ + y^\circ = 180^\circ$ Solving for $y^\circ$, $y^\circ = 180^\circ - 54^\circ - 60^\circ = 66^\circ$

2. For the second triangle (with angles $y^\circ = 66^\circ$, $65^\circ$, and $x^\circ$): Again, the sum of the angles in this triangle must also equal $180^\circ$. Therefore, $65^\circ + 66^\circ + x^\circ = 180^\circ$ Solving for $x^\circ$, $x^\circ = 180^\circ - 65^\circ - 66^\circ = 49^\circ$

Final answers:

• $y = 66^\circ$
• $x = 49^\circ$

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

Here are 5 related questions:

1. How do we calculate the exterior angle of a triangle?
2. What is the sum of interior angles in a polygon with 5 sides?
3. Can the triangle inequality theorem be applied to angle measurements?
4. What happens to the sum of angles in non-Euclidean geometries?
5. How would you approach solving for unknown angles in a quadrilateral?

Tip: Always remember, the sum of the angles in any triangle will always be $180^\circ$, regardless of its shape!