1. What is the sum of the three interior angles of any triangle?
- A90 deg
- B180 deg
- C270 deg
- D360 deg
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Answer: B) 180 deg
By the angle sum property of a triangle, the three interior angles always add up to 180 deg.
Class 7 Angle Sum Property — practice questions with answers
Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. The three angles of a triangle are in the ratio 1 : 2 : 3. The largest angle is:
- A60 deg
- B75 deg
- C90 deg
- D120 deg
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Answer: C) 90 deg
Let the angles be x, 2x, 3x. Then 6x = 180, x = 30. The largest is 3x = 90 deg.
3. If the angles of a triangle are all less than 90 deg, the triangle is called:
- Aright-angled
- Bacute-angled
- Cobtuse-angled
- Dscalene only
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Answer: B) acute-angled
A triangle with all angles less than 90 deg is an acute-angled triangle.
4. The angles of a triangle are (2x + 10) deg, (3x - 30) deg and (x + 20) deg.
Use the angle sum property to find x, then state the largest of the three angles.
Use the angle sum property to find x, then state the largest of the three angles.
- Ax = 30, largest 70 deg
- Bx = 30, largest 90 deg
- Cx = 25, largest 80 deg
- Dx = 35, largest 75 deg
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Answer: A) x = 30, largest 70 deg
(2x+10)+(3x-30)+(x+20) = 180 gives 6x = 180, so x = 30. The angles are 2(30)+10 = 70, 3(30)-30 = 60 and 30+20 = 50. The largest is 70 deg.
5. How many triangles are there whose three angles are all whole numbers of degrees, each a multiple of 30 deg, and each at least 30 deg (order of the three angles does not matter)?
List the angle-sums to check: each set must add to 180 deg.
List the angle-sums to check: each set must add to 180 deg.
- A1
- B2
- C3
- D4
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Answer: C) 3
Angles are multiples of 30 (30, 60, 90, 120) summing to 180. Valid unordered sets: {30, 30, 120}, {30, 60, 90}, {60, 60, 60}. That is 3 triangles.
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