To solve question 33, we analyze the given triangle. It is an isosceles triangle, as shown by the marks indicating two equal sides. In an isosceles triangle, the base angles are equal.

Steps to solve:

1. Let the unknown angles at the base be y° (both of them).

2. The sum of all angles in any triangle is $180^\circ$.

3. Thus, the equation for this triangle is:

   $y + y + x = 180$

   Since the vertex angle is $x^\circ$, the equation simplifies to:

   $2y + x = 180$

4. The problem does not provide a specific value for $x$, so we can only express $y$ in terms of $x$:

   $2y = 180 - x$

   $y = \frac{180 - x}{2}$

Final Answer:

• $y = \frac{180 - x}{2}$
• If a specific $x$ value is given, substitute it to calculate $y$.

Would you like to explore a scenario with a specific value for $x$? Let me know!

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Relative Questions:

1. What are the properties of isosceles triangles?
2. How can we prove the base angles are equal in isosceles triangles?
3. Can this approach be extended to solve scalene triangles?
4. How does the triangle sum theorem apply in 3D shapes?
5. What happens to the angles if the triangle becomes equilateral?

Tip: Always double-check whether any angles or side values are given in geometry problems to avoid overlooking key information!