The image shows a triangle problem where the top angle is 30°, and the sides opposite angles $x$ and $y$ are marked equal, indicating that this is an isosceles triangle. The question asks to select all correct options, and there may be multiple correct answers. Let's analyze the given options:

1. Given: The top angle of the triangle is 30°.
2. Isosceles triangle: Since two sides are equal, the angles opposite these equal sides (i.e., $x$ and $y$) must also be equal.
3. Sum of angles in a triangle: The sum of the interior angles of any triangle is always 180°.

Solution:

Since the top angle is 30°, the other two angles must satisfy: $x + y + 30^\circ = 180^\circ$ But since $x = y$ (from the isosceles property): $2x + 30^\circ = 180^\circ$ $2x = 150^\circ$ $x = 75^\circ$ Thus, both $x$ and $y$ are 75°.

Correct answers:

• A: $x = y$ is true because the triangle is isosceles.
• B: The other two angles are 75° is true.
• C: It's an isosceles triangle is true because two sides are equal.
• D: It's a scalene triangle is false because a scalene triangle has all sides and angles unequal, and this is not the case here.

Do you want more details or have any questions?

Here are some related questions to explore:

1. What is the general property of angles in any triangle?
2. How do we determine if a triangle is isosceles or scalene based on its angles?
3. How would this triangle change if the top angle were 60°?
4. What are the properties of a scalene triangle?
5. How would you calculate the area of this triangle if given the length of its sides?

Tip: Always check for the sum of interior angles in any triangle—they must add up to 180°.