Question 1: Calculate the third angle of a triangle if two angles measure 65° and 50°. Show your working.

Answer: 65

Question 2: In a triangle, one angle is 90° and another is 45°. What is the measure of the third angle?

Answer: 45

Question 3: Construct a triangle where one angle is 70°, another is 60°, and verify that the third angle makes the sum 180°.

Answer: 50

Question 4: If one exterior angle of a triangle measures 110°, what is the sum of the two non-adjacent interior angles?

Answer: 70

Question 1: Two angles of a triangle are 85° and 55°. Explain why the third angle must be less than 40° and calculate its exact measure.

Answer: 20

Question 2: A triangle has an exterior angle of 120°. If one of its interior opposite angles is 50°, find the other two interior angles.

Answer: 70 and 60

Question 3: Explain why the angles of a triangle cannot sum to more than 180° using examples or reasoning.

Answer: Angles in a triangle always sum to 180° because of the Euclidean geometry postulate; any deviation would contradict the definition of a triangle or the properties of Euclidean space.

Question 4: Construct a triangle where one angle is 40°, another 70°, and the third using the sum rule. Confirm the total is 180°.

Answer: 70

Question 1: A surveyor measures an angle of 125° at the corner of a triangular plot of land. The adjacent interior angles are supplementary. Find the two interior angles at this corner.

Answer: 55 and 0 (impossible, check assumptions)

Question 2: In a bridge design, two angles inside a triangular support are 80° and 60°. What is the measure of the third angle, and why is this important for structural stability?

Answer: 40; stability depends on correct angles to distribute load

Question 1: Prove that if two angles in a triangle are equal, the third angle is also equal, assuming the sum is 180°. Provide a detailed explanation.

Answer: The two equal angles imply the remaining angle is also equal because the total is 180°, so dividing the remaining degrees equally confirms equality.

Question 2: Given a triangle with angles measuring (x°, 2x°, 3x°), find the value of x.

Answer: 30

Question 1: A student states that the sum of angles in a triangle can be 200°. Identify the mistake and correct it.

Answer: Angles in a triangle always sum to 180°, mistake was assuming 200°.

Question 2: If an angle in a triangle is incorrectly calculated as 190°, what does this indicate about the problem?

Answer: It is impossible; angles in a triangle cannot exceed 180°, indicating a mistake in calculation or understanding.