Hard Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the measure of the complement of a 65° angle.
Correct! Complement = 90° - 65° = 25°.
(2) Write the measure of the supplement of a 125° angle.
Perfect! Supplement = 180° - 125° = 55°.
(3) How many right angles are there in a straight angle?
Excellent! 180° ÷ 90° = 2 right angles.
(4) Write the name of the angle which is greater than 180° but less than 360°.
Great! Reflex angles are between 180° and 360°.
(5) Write the measure of each angle in an equilateral triangle.
Correct! All angles in an equilateral triangle are 60°.
Short Answer Questions (2 Marks Each)
Answer each question with proper working
(1) Find the value of x if two complementary angles are x and 2x. x =
Perfect! x = 30°, so the angles are
(2) An angle is 45° more than its complement. Find the angle. Angle =
Excellent! The angle is 67.5°.
(3) Draw a triangle in which two angles are 60° and 75°. Find the third angle and classify the triangle based on its angles. Third angle =
(4) Draw two angles forming a linear pair. Measure each angle.
(5) Two supplementary angles are in the ratio 2:3. Find the angles. Smaller Angle:
Long Answer Questions (4 Marks Each)
Note: Answer each question with complete drawings, working, and clear explanations.
(1) Draw two parallel lines and a transversal. Mark and name all the pairs of corresponding, alternate interior, and co-interior angles.
(2) The measures of two angles of a triangle are 70° and 50°. Find the third angle and classify the triangle as acute, obtuse, or right-angled. Third angle =
Perfect! Since all angles (70°, 50°, 60°) are less than 90°, this is an
(3) One of the angles of a quadrilateral is 120° and the other three angles are equal. Find each of the equal angles. Each equal angle =
Excellent! Each equal angle measures 80°.
(4) The sum of an angle and its supplement is 180°. Prove this statement and give one example with a diagram.
(5) Draw two intersecting lines. Mark vertically opposite angles and show that they are equal by measurement.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) If one angle of a linear pair is 70°, the other angle is:
(a) 100° (b) 110° (c) 90° (d) 80°
Correct! Linear pair adds to 180°: 180° - 70° = 110°.
(2) The complement of a 30° angle is:
(a) 50° (b) 60° (c) 70° (d) 90°
Correct! Complement = 90° - 30° = 60°.
(3) Two angles are supplementary if their sum is:
(a) 90° (b) 120° (c) 150° (d) 180°
Correct! Supplementary angles always add up to 180°.
(4) The supplement of a right angle is:
(a) 45° (b) 60° (c) 90° (d) 120°
Correct! Supplement of 90° = 180° - 90° = 90°.
(5) The number of right angles in a complete revolution is:
(a) 2 (b) 3 (c) 4 (d) 6
Correct! 360° ÷ 90° = 4 right angles.
(6) If one angle of a triangle is 90°, the triangle is:
(a) Acute-angled (b) Obtuse-angled (c) Right-angled (d) Equilateral
Correct! A triangle with one 90° angle is right-angled.
(7) The sum of the angles of a quadrilateral is always:
(a) 180° (b) 270° (c) 360° (d) 540°
Correct! Sum of angles in any quadrilateral = 360°.
(8) An angle measuring more than 90° but less than 180° is called:
(a) Acute angle (b) Right angle (c) Obtuse angle (d) Straight angle
Correct! Obtuse angles are between 90° and 180°.
(9) If two lines intersect, the vertically opposite angles are:
(a) Equal (b) Supplementary (c) Complementary (d) Reflex
Correct! Vertically opposite angles are always equal.
(10) Which figure has all its angles equal and all its sides equal?
(a) Rectangle (b) Rhombus (c) Square (d) Parallelogram
Correct! A square has all sides equal and all angles equal (90°).
Solve and classify the following angle situations:
Complex Angle Relationships Challenge
Determine whether these statements are True or False:
Measures of Lines and Angles - Hard Quiz
🎉 Exceptional Mastery! Advanced Angle Concepts Conquered:
You have successfully mastered the "Measures of Lines and Angles (Hard)" worksheet and achieved:
(1) Advanced Angle Calculations: Solving complex problems involving complementary and supplementary angle relationships
(2) Algebraic Applications: Using variables to solve angle problems with ratios and unknown quantities
(3) Triangle Angle Properties: Applying the triangle angle sum theorem and classifying triangles by angles
(4) Quadrilateral Angle Analysis: Understanding that angles in any quadrilateral sum to 360°
(5) Linear Pair Recognition: Identifying and working with adjacent angles that form straight lines
(6) Parallel Line Geometry: Understanding corresponding, alternate interior, and co-interior angle relationships
(7) Vertically Opposite Angles: Proving and applying the equality of vertically opposite angles
(8) Complex Problem Solving: Solving multi-step problems involving multiple angle relationships
(9) Geometric Proofs: Understanding and constructing logical arguments for angle properties
(10) Ratio and Proportion: Solving angle problems where angles are given in specific ratios
(11) Triangle Classification: Categorizing triangles as acute, obtuse, or right-angled based on angle measures
(12) Advanced Construction: Drawing complex geometric figures with multiple angle relationships
(13) Equation Formation: Setting up and solving equations from geometric angle conditions
(14) Relationship Integration: Combining multiple geometric concepts to solve comprehensive problems
(15) Measurement Verification: Using geometric tools to verify theoretical calculations
(16) Mathematical Reasoning: Developing logical thinking skills through geometric problem-solving
Outstanding achievement! You've mastered advanced geometric reasoning with exceptional mathematical sophistication!