Angles and Geometry Practice

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Date:

⏱ 10-minute Warm-up: Quick Recall

1. Which statement is true?

A right angle equals 90°

A straight angle equals 90°

A full turn equals 90°

2. Two angles are complementary. If one is 35°, what is the other?

45°

55°

145°

3. In any triangle the sum of the interior angles is:

90°

180°

360°

✍️ Part 2: Worked Example & Guided Practice

Worked example (read carefully): A triangle has angles 48° and 67°. Find the third angle and explain your reasoning.

Solution: Sum of angles in a triangle = 180°. So third angle = 180° − (48° + 67°) = 180° − 115° = 65°. Reason: interior angles of triangle always add to 180°.

4. Guided practice — Find the missing angle in this triangle: two angles are 52° and 78°. Show your steps.

5. A straight line has two adjacent angles, one is 130°. What is the other? Explain why.

6. Two angles add to 180° and are called supplementary. If one angle is twice the other, find both angles and show algebraic working.

🔎 Part 3: Extension & Reasoning (Differentiation)

7. Parallel lines and a transversal: Alternate interior angles are equal. If two parallel lines are cut by a transversal and one interior angle is 110°, find the opposite interior angle and explain the reason using the parallel-lines rule.

8. Challenge — A quadrilateral has three interior angles of 85°, 105° and 60°. Find the fourth angle. Then state whether the shape could be a parallelogram and justify your answer.

9. Drawing task: Sketch a pair of intersecting lines that form vertical angles. Label one angle 47°. Measure and label all other angles that follow, and write one sentence explaining why opposite (vertical) angles are equal.