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About Triangles & Angle Properties — Class 7 CBSE

Classify triangles, explore angle sum property, and understand exterior angles. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 7). 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.

What you'll learn in Triangles & Angle Properties

  • Introduction to Triangles & Classification
  • The Angle Sum Property of a Triangle
  • Exterior Angle Property of a Triangle
  • Triangle Inequality Property
  • Combining Properties & Preparation for Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Triangles & Angle Properties — solved examples for Class 7 CBSE

Example 1easy

What is a defining characteristic of an acute-angled triangle?
  1. A)All angles are less than 90°.
  2. B)One angle is exactly 90°.
  3. C)One angle is greater than 90°.
  4. D)All sides are equal.

Step-by-step solution

  1. An acute angle is an angle that measures less than 90°.
  2. An acute-angled triangle is defined as a triangle where all three of its interior angles are acute.
  3. Therefore, in an acute-angled triangle, every angle must be less than 90°.

Answer: All angles are less than 90°.

Example 2medium

In a triangle, two angles measure 55° and 65°. What type of triangle is it?
  1. A)Acute-angled triangle
  2. B)Right-angled triangle
  3. C)Obtuse-angled triangle
  4. D)Equilateral triangle

Step-by-step solution

  1. Let the three angles of the triangle be A, B, and C. We are given A = 55° and B = 65°.
  2. Using the Angle Sum Property of a triangle, A + B + C = 180°.
    55°+65°+C=180°55° + 65° + C = 180°
  3. Calculate C: 120° + C = 180° ⇒ C = 180° - 120° = 60°.
  4. Since all three angles (55°, 65°, 60°) are less than 90°, the triangle is an acute-angled triangle.

Answer: Acute-angled triangle

Example 3hard

In triangle PQR, the angles are in the ratio 2:3:10. What type of triangle is PQR based on its angles?
  1. A)Acute-angled
  2. B)Right-angled
  3. C)Obtuse-angled
  4. D)Equilateral

Step-by-step solution

  1. Let the angles be 2x, 3x, and 10x.
  2. According to the Angle Sum Property, the sum of the angles in a triangle is 180°: 2x + 3x + 10x = 180°.
  3. Combine like terms: 15x = 180°. Solve for x: x = 180° / 15 = 12°.
  4. Calculate each angle: ∠P = 2 × 12° = 24°, ∠Q = 3 × 12° = 36°, ∠R = 10 × 12° = 120°. Since one angle (120°) is greater than 90°, the triangle is obtuse-angled.

Answer: Obtuse-angled

Practice questions on Triangles & Angle Properties

  1. Q1.easy

    Rohan claims that he drew a triangle with two obtuse angles. Is Rohan's claim possible?
    1. A)Yes, if the third angle is very small.
    2. B)Yes, if it's a very large triangle.
    3. C)No, because the sum of two obtuse angles would already exceed 180°.
    4. D)No, because triangles can only have one right angle.
    Show answer

    Answer: No, because the sum of two obtuse angles would already exceed 180°.

    Hint: An obtuse angle is greater than 90°. Consider the angle sum property of a triangle.

  2. Q2.easy

    In triangle PQR, ∠P = 45° and ∠Q = 65°. What is the measure of ∠R?
    1. A)70°
    2. B)80°
    3. C)60°
    4. D)90°
    Show answer

    Answer: 70°

    Hint: Apply the angle sum property of a triangle.

  3. Q3.easy

    An exterior angle of a triangle is 120°. If one of its interior opposite angles is 70°, what is the measure of the other interior opposite angle?
    1. A)40°
    2. B)50°
    3. C)60°
    4. D)70°
    Show answer

    Answer: 50°

    Hint: Recall the exterior angle property, which relates an exterior angle to its two interior opposite angles.

  4. Q4.medium

    A triangle has side lengths of 8 cm, 8 cm, and 10 cm. Which of the following statements is TRUE about this triangle?
    1. A)It is a scalene triangle.
    2. B)It is an equilateral triangle.
    3. C)It is an isosceles triangle.
    4. D)It is a right-angled triangle.
    Show answer

    Answer: It is an isosceles triangle.

    Hint: Recall the definitions of different types of triangles based on their side lengths.

  5. Q5.medium

    The angles of a triangle are in the ratio 2 : 3 : 5. Find the measure of the largest angle.
    1. A)36°
    2. B)54°
    3. C)90°
    4. D)180°
    Show answer

    Answer: 90°

    Hint: Represent the angles using the given ratio and then apply the angle sum property of a triangle.

  6. Q6.medium

    In triangle PQR, side QR is extended to a point S. If ∠P = 70° and ∠Q = 60°, what is the measure of the exterior angle ∠PRS?
    1. A)110°
    2. B)120°
    3. C)130°
    4. D)140°
    Show answer

    Answer: 130°

    Hint: Remember the Exterior Angle Property of a triangle, which relates an exterior angle to its opposite interior angles.

  7. Q7.hard

    In triangle PQR, side QR is extended to point S. If the exterior angle ∠PRS = 110° and ∠Q = 65°, what is the measure of ∠P and what type of triangle is PQR?
    1. A)∠P = 45°, Acute-angled
    2. B)∠P = 45°, Obtuse-angled
    3. C)∠P = 55°, Right-angled
    4. D)∠P = 55°, Acute-angled
    Show answer

    Answer: ∠P = 45°, Acute-angled

    Hint: Recall the Exterior Angle Property of a triangle. Also, remember that angles on a straight line sum to 180°.

  8. Q8.hard

    Triangle ABC is isosceles with AB = AC. Side BC is extended to point D. If ∠ACD = 108°, find the measure of ∠BAC.
    1. A)36°
    2. B)72°
    3. C)54°
    4. D)42°
    Show answer

    Answer: 36°

    Hint: Start by finding the interior angle ∠ACB using the linear pair property. Then use the property of isosceles triangles regarding angles opposite equal sides.

  9. Q9.hard

    In triangle ABC, AB = AC and ∠BAC = 20°. Point D is on AC such that BD = BC. Find the measure of ∠ABD.
    1. A)20°
    2. B)30°
    3. C)40°
    4. D)60°
    Show answer

    Answer: 60°

    Hint: This problem involves multiple isosceles triangles. Carefully find angles in the larger triangle first, then in the smaller one, and use subtraction.

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