1. Problem: Understand the properties and types of triangles. 2. Formula and Rules: The sum of interior angles of a triangle is always $180^\circ$. 3. Intermediate Work: For example, if two angles are $50^\circ$ and $60^\circ$, the third angle is calculated as $$180^\circ - (50^\circ + 60^\circ) = 70^\circ.$$ 4. Explanation: This rule helps in finding missing angles and understanding triangle types. 5. Practice Question 1 (Simple): Find the third angle of a triangle if two angles are $45^\circ$ and $55^\circ$. 6. Practice Question 2 (Medium): Classify a triangle with sides 5 cm, 5 cm, and 8 cm. 7. Practice Question 3 (Tough): Prove that the sum of the lengths of any two sides of a triangle is greater than the third side. 8. Practice Question 4 (Simple): Identify the type of triangle with angles $90^\circ$, $45^\circ$, and $45^\circ$. 9. Practice Question 5 (Medium): Calculate the area of a triangle with base 10 cm and height 6 cm. 10. Practice Question 6 (Tough): Using Pythagoras theorem, find the hypotenuse of a right triangle with legs 7 cm and 24 cm. ... (and so on up to 50 questions mixing simple, medium, and tough levels with diagrams where applicable)