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About Geometric Properties — Class 8 IB

Explore properties of triangles, quadrilaterals, and polygons with formal reasoning. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 5). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Geometric Properties — solved examples for Class 8 IB

Example 1easy

What is the sum of interior angles of a triangle?
  1. A)90°
  2. B)180°
  3. C)270°
  4. D)360°

Step-by-step solution

  1. The sum of interior angles in any triangle is 180°.

Answer: 180°

Example 2medium

Find the sum of interior angles of an octagon.
  1. A)720°
  2. B)900°
  3. C)1080°
  4. D)1260°

Step-by-step solution

  1. Sum:
    (8−2)×180°=1080°(8-2) \times 180° = 1080°

Answer: 1080°

Example 3hard

The interior angle of a regular polygon is 5 times its exterior angle. How many sides does it have?
  1. A)10
  2. B)12
  3. C)15
  4. D)18

Step-by-step solution

  1. Let exterior = x. Then 5x + x = 180° so x = 30°.
    n=360°30°=12n = \frac{360°}{30°} = 12

Answer: 12

Practice questions on Geometric Properties

  1. Q1.easy

    What is the sum of interior angles of a quadrilateral?
    1. A)180°
    2. B)270°
    3. C)360°
    4. D)540°
    Show answer

    Answer: 360°

    Hint: A quadrilateral can be split into two triangles.

  2. Q2.easy

    Two angles on a straight line add up to?
    1. A)90°
    2. B)180°
    3. C)270°
    4. D)360°
    Show answer

    Answer: 180°

    Hint: A straight line forms a straight angle.

  3. Q3.easy

    Vertically opposite angles are:
    1. A)Supplementary
    2. B)Complementary
    3. C)Equal
    4. D)Right angles
    Show answer

    Answer: Equal

    Hint: When two lines cross, they form two pairs of equal angles.

  4. Q4.medium

    Each interior angle of a regular polygon is 108°. How many sides does it have?
    1. A)4
    2. B)5
    3. C)6
    4. D)8
    Show answer

    Answer: 5

    Hint: Use the formula: each interior angle = (n-2) x 180° / n.

  5. Q5.medium

    Two parallel lines are cut by a transversal. One of the alternate angles is 65°. What is the co-interior angle on the same side?
    1. A)65°
    2. B)115°
    3. C)125°
    4. D)180°
    Show answer

    Answer: 115°

    Hint: Co-interior angles are supplementary to alternate angles on the same side.

  6. Q6.medium

    In triangle ABC, angle A = 50° and angle B = 70°. Find the exterior angle at C.
    1. A)60°
    2. B)110°
    3. C)120°
    4. D)130°
    Show answer

    Answer: 120°

    Hint: The exterior angle equals the sum of the two non-adjacent interior angles.

  7. Q7.hard

    In the figure, two parallel lines are cut by two transversals. Angle A = 50° and angle B = 70°. Find angle C formed between the transversals between the parallel lines.
    1. A)60°
    2. B)110°
    3. C)120°
    4. D)130°
    Show answer

    Answer: 120°

    Hint: Use the triangle formed between the parallel lines. The angles at the parallel lines are related to A and B.

  8. Q8.hard

    Find the number of sides of a polygon whose interior angles sum to 2340°.
    1. A)13
    2. B)14
    3. C)15
    4. D)16
    Show answer

    Answer: 15

    Hint: Use (n-2) x 180° = 2340°.

  9. Q9.hard

    In a regular pentagon, find the angle at the tip of each triangular section when diagonals are drawn from one vertex.
    1. A)36°
    2. B)54°
    3. C)72°
    4. D)108°
    Show answer

    Answer: 36°

    Hint: Each triangle at the tip has the base angles related to the interior angle.

These are 9 of the 60 questions available for Geometric Properties. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.