Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Define adjacent angles. Two angles that share a common
Perfect! Adjacent angles share a vertex and side without overlapping.
(2) Define linear pair of angles. Two
Excellent! A linear pair consists of adjacent angles that sum to 180°.
(3) What is the sum of the measures of the angles around a point?
Correct! The sum of angles around a point is always 360°.
(4) State the condition for two angles to be supplementary. The
Great! Two angles are supplementary if their sum equals 180°.
(5) Name the angles that form a linear pair when two lines intersect.
Perfect! When two lines intersect, adjacent angles form linear pairs.
Short Answer Questions (2 Marks Each)
Answer each question with detailed steps
(1) Two supplementary angles are in the ratio 7 : 8. Find the angles.
Smaller angle:
Larger angle:
Excellent! The angles are 84° and 96°.
(2) If one of the complementary angles is 4x° and the other is (3x - 10)°, find x. x =
Great! The value of x is
(3) Two vertically opposite angles are (x + 15)° and (2x - 25)°. Find x and the angles. x =
Perfect! x = 40° and each angle measures 55°.
(4) The sum of the measures of two angles is 130° and their difference is 30°. Find the angles.
Excellent! The angles are 80° and 50°.
(5) If two lines intersect, prove that each pair of vertically opposite angles is equal.
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete proof/detailed steps and clear explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Prove that the sum of all the angles formed on one side of a straight line is 180°.
(2) Two supplementary angles differ by 42°. Find the angles and show that their sum is 180°. Smaller Angle =
Perfect! The angles are 111° and 69°, and their sum is 180°.
(3) Lines AB and CD intersect at O. If ∠AOC = (5x - 20)° and ∠BOD = (3x + 40)°, find x and the angles. x =
Excellent! x = 30°, and the angles are 130°, 50°, 130°, 50°.
(4) The complement of an angle is 20° more than twice the angle. Find the angle. Angle =
Great! The angle is
(5) Lines PQ and RS intersect at O. If ∠POR = 70°, find all the other angles. Justify your answer. Angles:
Perfect! The angles are: 70°, 110°, 70°, 110°.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) Adjacent angles have:
(a) A common vertex only (b) A common side only (c) A common vertex and a common side (d) No common elements
Correct! Adjacent angles share both a common vertex and a common side.
(2) The sum of angles around a point is:
(a) 90° (b) 180° (c) 270° (d) 360°
Correct! The sum of angles around a point is always 360°.
(3) Two angles form a linear pair if:
(a) They are equal (b) They are complementary (c) Their non-common arms form a straight line (d) They are vertically opposite angles
Correct! Linear pair angles have non-common arms forming a straight line.
(4) If two lines are intersecting, how many linear pairs are formed?
(a) 1 (b) 2 (c) 3 (d) 4
Correct! Two intersecting lines form 4 linear pairs.
(5) If one of the angles in a linear pair is 110°, then the other is:
(a) 70° (b) 60° (c) 80° (d) 50°
Correct! Linear pair angles sum to 180°: 180° - 110° = 70°.
(6) The supplement of 75° is:
(a) 95° (b) 105° (c) 85° (d) 115°
Correct! Supplement of 75° = 180° - 75° = 105°.
(7) The complement of 65° is:
(a) 35° (b) 25° (c) 45° (d) 55°
Correct! Complement of 65° = 90° - 65° = 25°.
(8) Vertically opposite angles are:
(a) Equal (b) Supplementary (c) Complementary (d) Right angles
Correct! Vertically opposite angles are always equal.
(9) If the sum of two angles is 180°, then they are:
(a) Complementary (b) Supplementary (c) Equal (d) Right
Correct! Two angles that sum to 180° are supplementary.
(10) In a linear pair, if one angle is x, the other is:
(a) 90 - x (b) 180 - x (c) x - 90 (d) x + 90
Correct! In a linear pair, if one angle is x, the other is 180° - x.
Let's practice advanced angle relationships!!!
Excellent! You understand the distinctions between different angle relationships.
Advanced True or False: Angle Properties
Determine whether these complex statements are True or False:
Comprehensive Advanced Quiz
🎉 You Did It! What You've Mastered:
By completing this advanced worksheet, you now have expert knowledge of:
(1) Advanced Angle Definitions: Adjacent angles, linear pairs, and their properties
(2) Complex Angle Relationships: Multiple intersecting lines and angle formations
(3) Algebraic Problem Solving: Using ratios and equations to find unknown angles
(4) Geometric Proofs: Understanding and constructing logical arguments
(5) Linear Pair Properties: Adjacent supplementary angles on straight lines
(6) Multiple Line Intersections: Analyzing complex geometric configurations
(7) Real-World Applications: Solving practical problems involving angle relationships
(8) Advanced Calculations: Working with fractions, ratios, and complex expressions
(9) Critical Thinking: Distinguishing between different types of angle relationships
(10) Problem Verification: Checking solutions and understanding geometric principles
Outstanding work conquering advanced lines and angles concepts!