Question 1: Calculate the value of the unknown angle in the diagram where two angles are 120° and 80° at a point.

Answer: 160

Question 2: In a diagram, four angles at a point are 90°, 85°, ?°, and 100°. Find the missing angle.

Answer: 85

Question 3: Construct an angle at a point where three angles are 150°, 90°, and ?. Show your working.

Answer: 120

Question 4: In a regular polygon, the angles around a point are all equal. If four such angles meet at a point, what is each angle?

Answer: 90

Question 5: A clock's minute hand points at 12 and hour hand at 3. What is the angle between them? (Use the concept of angles summing to 360° at a point.)

Answer: 90

Question 6: A teacher draws a diagram with three angles at a point measuring 130°, 70°, and ?. Find the missing angle.

Answer: 160

Question 7: A multi-step problem: Two angles at a point are 75° and 105°. A third angle is supplementary to the first. What is the measure of the third angle?

Answer: 105

Question 8: In a diagram, two angles are 200° and ?. The remaining two angles at the point are equal. Calculate the measure of each of the equal angles.

Answer: 80

Question 9: Real-world application: A circular table is divided into sections, each with angles at a point summing to 360°. If one section is 110°, what is the combined measure of the other sections assuming there are three remaining sections?

Answer: 250

Question 10: Challenge: Two angles at a point are 220° and ?. The remaining angles are each 70°. Find the missing angle.

Answer: 70

Question 11: Error Analysis: A student claims that angles at a point can sum to anything other than 360°. Explain the mistake and correct it.

Answer: Angles at a point always sum to 360° because they form a full rotation around a point.