Question 1: Calculate the missing angle at a point if four angles are 80°, 100°, 50°, and x°. Write your answer for x°.

Answer: 130

Question 2: If three angles at a point are 125°, 90°, and y°, find the value of y°.

Answer: 145

Question 3: Construct an angle that is exactly 60°, and then mark a second angle that makes the total 360° when combined with the first.

Answer: 300

Question 4: In a diagram, three angles at a point are 85°, 150°, and z°. Calculate z°.

Answer: 125

Question 1: Two angles at a point are 40° and 75°. The remaining angles are all equal. Find the measure of each of these equal angles.

Answer: 81.25

Question 2: In a diagram, five angles at a point are marked as 2x°, 3x°, 4x°, 5x°, and 6x°. Confirm that their total is 360° and find the value of x°.

Answer: 10

Question 3: A clock shows the hour hand at 2 o'clock. The minute hand points at 12. If the hands form an angle of 60°, what is the angle between the two hands at 2:10? Explain your reasoning.

Answer: The angle is 35°. Explanation: The hour hand moves 0.5° per minute, so at 2:10, it is at 2*30 + 10*0.5=60+5=65°. The minute hand is at 0°, so the difference is |65−0|=65°. Since angles are measured clockwise, the smaller angle is 60°, but the actual difference at 2:10 is 35° because the hour hand has moved slightly towards 3 o'clock, and the exact calculation accounts for that movement.

Question 1: A car's steering wheel is turned so that the angles between the spokes are 90°, 60°, and the remaining angle at the centre of the wheel. What is the measure of the remaining angle?

Answer: 210

Question 2: In a circular park, four paths meet at a central point forming angles of 100°, 80°, and 70°. Find the measure of the fourth angle, and explain how you determine it.

Answer: 110

Question 1: Construct a diagram where four angles at a point are in the ratio 1:2:3:4. Using the grid, mark and calculate each angle.

Answer: 45°, 90°, 135°, 180°

Question 2: The sum of three angles at a point is 250°. Two of the angles are equal, and the third is 80°. Find the measure of each of the equal angles.

Answer: 85

Question 1: If one angle at a point is 150°, what are the measures of the other angles if they are all equal?

Answer: 30

Question 2: Explain why the angles at a point always sum to 360°, using a real-world analogy or a simple diagram.

Answer: [Expected explanation: Like slices of a pizza; all slices together make a full circle of 360°.]

Question 1: A student calculates that the angles at a point are 90°, 100°, 80°, and 70° and claims the total is 340°. Identify the mistake and correct the calculation.

Answer: The mistake is summing only four angles, but the total must be 360°. The correct total is 90+100+80+70=340°, so the missing angle is 20°.