Question 1: If three angles at a point measure 80°, 120°, and x°, find the value of x°.

Answer: 160

Question 2: Calculate the missing angle if two angles at a point are 75° and 150°.

Answer: 135

Question 3: Construct a diagram on the grid showing four angles at a point measuring 90°, 60°, 100°, and x°. Find x°.

Answer: 110

Question 4: In a circle, three angles at a point sum to 280°. What is the measure of the remaining angle?

Answer: 80

Question 5: A point has four angles measuring 85°, x°, 105°, and y°. If x = 2y, find the values of x and y.

Answer: 85, 70

Question 6: A polygon has several angles at a point, one of which is 150°. If all other angles sum to 210°, what is the total sum of all the angles at that point?

Answer: 360

Question 7: A set of angles at a point are in the ratio 1:2:3, and their total is 360°. Find the measures of each angle.

Answer: 60, 120, 180

Question 8: A real-world scenario: A clock's hands form angles at a point. If the minute hand and hour hand form an angle of 150°, how many degrees is the smaller angle between them?

Answer: 150

Question 9: Identify the common mistake: A student claims that the sum of angles at a point can be more than 360°. Explain and correct this misconception.

Answer: Angles at a point always sum to 360°. The student’s mistake is assuming they can sum to more than 360°, but in reality, the total is fixed at 360°.

Question 10: Given two angles at a point are 200° and 50°, find the measure of the third angle and explain your reasoning.

Answer: 110

Question 11: Challenge: Three angles at a point are in the ratio 3:4:5. If their sum is less than 360°, what is the total sum, and what are the individual angles?

Answer: Total sum: 360°, angles: 108°, 144°, 180°