Question 1: Calculate the missing angle in a quadrilateral where three angles are 80°, 100°, and 70°. Show your working.

Answer: 110

Question 2: A quadrilateral has three angles measuring 90°, 85°, and 95°. What is the measure of the fourth angle?

Answer: 90

Question 3: Explain why the sum of interior angles in any quadrilateral is always 360°.

Answer: In any quadrilateral, the sum of interior angles is 360° because when you divide the quadrilateral into two triangles, the sum of angles in each triangle is 180°, so total is 2×180°=360°.

Question 4: A quadrilateral has one angle of 120°. If the other three angles are equal, what are their measures? Show your calculations.

Answer: 40

Question 5: A student claims that a quadrilateral with angles 90°, 90°, 90°, and 90° does not have a sum of 360°. Is this true? Explain your reasoning.

Answer: The statement is false because 90°+90°+90°+90°=360°, which is the correct sum for a quadrilateral.

Question 6: Construct a quadrilateral where two adjacent angles are each 110°. Calculate the remaining two angles.

Answer: 70 and 70

Question 7: A quadrilateral has angles measuring 80°, 85°, 95°, and a missing angle. What is the missing angle? Show your working.

Answer: 100

Question 8: Identify and correct the mistake in the following reasoning: 'Since one angle is 100°, the other three must sum to 260°, so each could be 86.67°'.

Answer: The mistake is assuming the other three angles are equal; they could be different. The correct total for the other three angles is 260°, but they can vary in measurement.

Question 9: A quadrilateral has two angles of 85° and 105°. If the other two angles are equal, find their measures.

Answer: 85

Question 10: A trapezium has interior angles of 70°, 110°, and two unknown angles. If the interior angles in total sum to 360°, what are the measures of the unknown angles?

Answer: 90 and 90

Question 11: A common misconception is that the sum of interior angles in a quadrilateral can be more than 360°. Explain why this is incorrect.

Answer: It is incorrect because the sum of interior angles in any quadrilateral is always 360°, as proven by dividing it into two triangles, each with a sum of 180°.