Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) State the angle sum property of a triangle.
The
Perfect! This is one of the most fundamental properties in geometry.
(2) Define alternate interior angles.
Alternate interior angles are pairs of angles that lie on
Excellent! This property is crucial for proving lines are parallel.
(3) What is the angle formed by the hands of a clock at 9 o'clock?
Correct! At 9 o'clock, the hands form a right angle.
(4) List out the angles formed when a transversal cuts two lines.
Total number of angles formed:
Perfect! A transversal creates 4 angles at each intersection point.
(5) What is the measure of an angle if its supplement is three times its complement?
Excellent! Let angle = x, then (180-x) = 3(90-x), solving gives x = 45°.
Short Answer Questions (2 Marks Each)
Answer each question in 2-3 sentences
(1) If two lines are parallel and a transversal intersects them forming one angle of 75°, find the corresponding angle.
Corresponding angles are
Therefore, the corresponding angle =
Correct! Corresponding angles are always equal when lines are parallel.
(2) Prove that if two lines intersect, the vertically opposite angles are equal.
(3) If two angles are supplementary and one is 20° more than the other, find the angles.
Smaller angle:
Larger angle:
Excellent work! Always verify: 80° + 100° = 180°.
(4) In a triangle, one angle is 90°, and another is 45°. Find the third angle and classify the triangle.
Third angle =
Classification:
Perfect! It's right-angled (has 90°) and isosceles (two equal 45° angles).
(5) Draw a diagram to show a pair of adjacent supplementary angles and label them.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Lines AB and CD intersect at point O. If ∠AOC = 50° and ∠BOE = 130°, show that AB and CD are straight lines.
(2) Two angles form a linear pair. One angle is four times the other. Find both angles and prove they form a linear pair.
Smaller angle:
Larger angle:
Verification: 36° + 144° = 180°
(3) A transversal intersects two lines. The alternate interior angles are equal. Prove that the lines are parallel.
(4) In triangle ABC, ∠A = 50°, ∠B = 60°. Find ∠C. Then find the exterior angle at vertex C and verify the exterior angle property.
∠C =
Exterior angle at C =
Verification: Exterior angle = ∠A + ∠B = 50° + 60° = 110°
Perfect! The exterior angle equals the sum of the two opposite interior angles.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) If two angles are vertically opposite and one is 120°, the other is:
(a) 120° (b) 60° (c) 90° (d) 180°
Correct! Vertically opposite angles are always equal.
(2) Which of the following statements is true?
(a) Adjacent angles are always equal (b) Linear pair angles are complementary (c) Vertically opposite angles are equal (d) Supplementary angles are always equal
Correct! This is a fundamental property of intersecting lines.
(3) If two lines are cut by a transversal and alternate interior angles are equal, then the lines are:
(a) Perpendicular (b) Intersecting (c) Parallel (d) Coinciding
Correct! Equal alternate interior angles prove lines are parallel.
(4) In triangle PQR, if ∠P = 40°, ∠Q = 70°, then ∠R =
(a) 70° (b) 60° (c) 80° (d) 90°
Correct! 40° + 70° + 70° = 180°. Wait, let me recalculate: 40° + 70° = 110°, so ∠R = 180° - 110° = 70°.
(5) The sum of the measures of the angles on a straight line is:
(a) 180° (b) 360° (c) 90° (d) 0°
Correct! A straight line forms a straight angle of 180°.
(6) Two angles are supplementary. If one angle is 3x and the other is 2x, then the value of x is:
(a) 36° (b) 72° (c) 45° (d) 60°
Correct! 3x + 2x = 180°, so 5x = 180°, therefore x = 36°.
(7) Which of the following is not a pair of adjacent angles?
(a) ∠AOB and ∠BOC on a straight line (b) ∠P and ∠Q with same vertex and common arm (c) Vertically opposite angles (d) ∠X and ∠Y sharing one ray and one vertex
Correct! Vertically opposite angles are opposite each other, not adjacent.
(8) If two lines are parallel, the corresponding angles are:
(a) Unequal (b) Complementary (c) Equal (d) None
Correct! Corresponding angles are equal when lines are parallel.
(9) ∠1 and ∠2 form a linear pair. If ∠1 = (2x + 10)°, ∠2 = (x - 20)°, then x =
(a) 30 (b) 40 (c) 50 (d) 60
Correct! (2x + 10) + (x – 20) = 180 ⟹ 3x – 10 = 180 → 3x = 190 → x = 50
(10) The exterior angle of a triangle is equal to:
(a) The adjacent angle (b) Sum of two interior opposite angles (c) Half of the base angle (d) Supplement of the base angle
Correct! This is the exterior angle theorem - a fundamental property of triangles.
Lines and Angles Challenge
Determine whether these statements about lines and angles are True or False: