Question 1: In a quadrilateral, three angles measure 80°, 90°, and 100°. Find the measure of the unknown angle.

Answer: 90

Question 2: A quadrilateral has angles measuring 110°, 75°, and an unknown angle. What is the measure of the unknown angle?

Answer: 100

Question 3: Calculate the missing angle in a quadrilateral where the other three angles are 85°, 95°, and 75°.

Answer: 105

Question 4: Construct a quadrilateral where three angles are 90°, 80°, and 70°. Draw and shade the shape on the grid, then find the measure of the fourth angle.

Answer: 120

Question 5: A rectangle has one corner with an external angle measuring 70°. What is the interior angle at that corner?

Answer: 110

Question 6: A parallelogram has two angles measuring 65° and 115°. Find the measures of the other two angles.

Answer: 115 and 65

Question 7: A shape is made of four angles, two measuring 80° and two measuring 100°. Verify that the angles sum to 360° and explain why this confirms the shape is a quadrilateral.

Answer: Sum = 80 + 80 + 100 + 100 = 360°, which confirms it is a quadrilateral because the interior angles sum to 360°.

Question 8: A regular hexagon is drawn on the grid. Sketch it and then calculate the sum of the interior angles of the hexagon.

Answer: 720

Question 9: A quadrilateral has two adjacent angles measuring 85° and 95°. If the other two angles are equal, find their measures and verify the total sum.

Answer: 90° and 85°, sum = 360°

Question 10: Identify and correct the mistake: A student claims the angles of a quadrilateral are 85°, 95°, 100°, and 90°, and that these sum to 360°. The student wrote 'Total = 370°'. What is the mistake, and what should the correct total be?

Answer: Mistake: Incorrect addition. Correct total: 85 + 95 + 100 + 90 = 370°, which is actually incorrect. The correct total should be 360°, so the student made a miscalculation.

Question 11: Design a complex quadrilateral with one interior angle of 120° and three other angles with known measures. Calculate the remaining angles ensuring the sum is 360°.

Answer: The other three angles could be 80°, 70°, and 90° (for example).