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## The Triangle and its Properties Class 7 Maths MCQs Pdf

**1.** How many elements are there in a triangle?

**(a)** 3

**(b)** 6

**(c)** 4

**(d)** None of these.

**Answer/Explanation**

Answer: (b)

Explanation : See a triangle.

**2.** How many vertices does a triangle have?

**(a)** 1

**(b)** 2

**(c)** 3

**(d)** 4

**Answer/Explanation**

Answer: (c)

Explanation : See a triangle.

**3.** How many sides are there in a triangle?

**(a)** 1

**(b)** 2

**(c)** 3

**(d)** 4

**Answer/Explanation**

Answer: (c)

Explanation : See a triangle.

**4.** How many angles are there in a triangle?

**(a)** 1

**(b)** 2

**(c)** 3

**(d)** 4

**Answer/Explanation**

Answer: (c)

Explanation : See a triangle.

**5.** If two sides of a triangle are not equal, the triangle is called

**(a)** scalene

**(b)** isosceles

**(c)** equilateral

**(d)** right-angled

**Answer/Explanation**

Answer: (a)

Explanation : Definition of a scalene triangle.

**6.** If two sides of a triangle are equal, the triangle is called

**(a)** isosceles

**(b)** equilateral

**(c)** scalene

**(d)** right-angled

**Answer/Explanation**

Answer: (a)

Explanation : Definition of an isosceles triangle.

**7.** If all the three sides of a triangle are equal, the triangle is called

**(a)** equilateral

**(b)** right-angled

**(c)** isosceles

**(d)** scalene

**Answer/Explanation**

Answer: (a)

Explanation : Definition of an equilateral triangle.

**8.** If all the angles of a triangle are acute, the triangle is called

**(a)** obtuse-angled

**(b)** acute-angled

**(c)** right-angled

**(d)** none of these

**Answer/Explanation**

Answer: (b)

Explanation : Definition of an acute-angled triangle.

**9.** If one angle of a triangle measures 90°, the triangle is called

**(a)** acute-angled

**(b)** obtuse-angled

**(c)** right-angled

**(d)** none of these

**Answer/Explanation**

Answer: (c)

Explanation : Definition of a right triangle.

**10.** If one angle of a triangle is obtuse, the triangle is called

**(a)** acute-angled

**(b)** obtuse-angled

**(c)** right-angled

**(d)** none of these

**Answer/Explanation**

Answer: (b)

Explanation : Definition of an obtuse angled triangle.

**11,** How many medians can a triangle have?

**(a)** 1

**(b)** 2

**(c)** 3

**(d)** 4

**Answer/Explanation**

Answer: (c)

Explanation : Draw medians and count.

**12.** How many altitudes can a triangle have?

**(a)** 1

**(b)** 2

**(c)** 3

**(d)** 4

**Answer/Explanation**

Answer: (c)

Explanation : Draw altitudes and count.

**13.** The total measure of the three angles of a triangle is

**(a)** 360°

**(b)** 90°

**(c)** 180°

**(d)** none of these

**Answer/Explanation**

Answer: (c)

Explanation : Angle Sum Property of a triangle.

**14.** The measure of each angle of an equilateral triangle is

**(a)** 30°

**(b)** 45°

**(c)** 90°

**(d)** 60°

**Answer/Explanation**

Answer: (d)

Explanation : x° + x° + x° = 180° ⇒ x° = 60°.

**15.** Which of the following statements is true?

**(a)** A triangle can have two right angles

**(b)** A triangle can have two obtuse angles

**(c)** A triangle can have two acute angles

**(d)** A triangle can have all the three angles less than 60°

**Answer/Explanation**

Answer: (c)

Explanation :

**16.** Which of the following statements is true?

**(a)** A triangle can have all the three angles equal to 60°.

**(b)** A triangle can have all the three angles greater than 60°.

**(c)** The sum of any two angles of a triangle is always greater than the third angle.

**(d)** The difference between the lengths of any two sides of a triangle is greater than the length of the third side

**Answer/Explanation**

Answer: (a)

Explanation :

**17.** Which of the following statement is false?

**(a)** The sum of the lengths of any two sides of a triangle is less than the third side.

**(b)** In a right-angled triangle, the square on the hypotenuse = sum of the squares on the legs.

**(c)** If the Pythagorean property holds, the triangle must be right-angled.

**(d)** The diagonal of a rectangle produce ‘by itself the same area as produced by its length and breadth

**Answer/Explanation**

Answer: (a)

Explanation :

**18.** Two angles of a triangle measure 90° and 30°. The measure of the third angle is

**(a)** 90°

**(b)** 30°

**(c)** 60°

**(d)** 120°

**Answer/Explanation**

Answer: (c)

Explanation : Third angle = 180° – (90° + 30°) = 60°.

**19.** The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is

**(a)** 80°

**(b)** 60°

**(c)** 40°

**(d)** 180°

**Answer/Explanation**

Answer: (a)

Explanation : Largest angle = \(\frac { 4 }{ 2+3+4 } \) × 180° = 80°.

**20.** In the following figure, the side BC of ∆ ABC is extended up to the point D. If ∠ A = 55° and ∠ B = 60°, then the measure of ∠ACD is

**(a)** 120°

**(b)** 110°

**(c)** 115°

**(d)** 125°

**Answer/Explanation**

Answer: (c)

Explanation : ∠ ACD = 60° + 55° = 115°.

**21.** In the following figure, the measure of ∠A is

**(a)** 30°

**(b)** 45°

**(c)** 90°

**(d)** 30°

**Answer/Explanation**

Answer: (d)

Explanation : ∠ A – 180° – [(180° – 120°) + (180° – 120°)] = 60°.

**22.** In the following figure, the measure of ∠A is

**(a)** 70°

**(b)** 90°

**(c)** 80°

**(d)** 100°

**Answer/Explanation**

Answer: (c)

Explanation : ∠A – 180° – (60° + 40°) = 80°

**23.** In the following figure, m || QR. Then, the measure of ∠QPR is

**(a)** 80°

**(b)** 85°

**(c)** 75°

**(d)** 70°

**Answer/Explanation**

Answer: (b)

Explanation : ∠ PQR = 50°

∴ ∠ QPR – 180° – (50° + 45°) = 85°.

**24.** In the following figure, find ∠ x and ∠ y, if ∠x – ∠y – 10°

**(a)** 65°, 55°

**(b)** 55°, 45°

**(c)** 45°, 35°

**(d)** 60°, 60°

**Answer/Explanation**

Answer: (a)

Explanation : ∠x + ∠y = 120°; ∠x – ∠y = 10° Solve to get ∠x = 65°, ∠y = 55°.

**25.** In the following figure, find ∠ B.

**(a)** 30°

**(b)** 45°

**(c)** 40°

**(d)** 60°

**Answer/Explanation**

Answer: (d)

Explanation : ∠B = 180° – [(180° – 110°) + 50°] = 60°.

**26.** In the following figure, ∆ ABC is an equilateral triangle. Find ∠x.

**(a)** 30°

**(b)** 45°

**(c)** 60°

**(d)** 90°

**Answer/Explanation**

Answer: (a)

Explanation : ∠ABC = 60°.

∴ ∠ABD = 180° – 60° = 120°

∴ x = 180° – (120° + 30°) = 30°.

**27.** In the following figure, one angle of triangle ABC is 40°. If the difference of the other two angles is 30°, find the larger of the other two angles.

**(a)** 85°

**(b)** 80°

**(c)** 75°

**(d)** 70°

**Answer/Explanation**

Answer: (a)

Explanation : x + y = 180° – 40° = 140° x – y = 30°. Solve to get x = 85°.

**28.** In the following figure, find

**(a)** 60°

**(b)** 70°

**(c)** 80°

**(d)** 75°

**Answer/Explanation**

Answer: (b)

Explanation : x + x = 140° ⇒ x = 70°.

**29.** In the following figure, find x if BA || CE.

**(a)** 60°

**(b)** 40°

**(c)** 45°

**(d)** 65°

**Answer/Explanation**

Answer: (d)

Explanation : ∠ECD = ∠ABC = 50°;

∴ x = 180° – (65° + 50°) = 65°.

**30.** Find the value of the unknown interior angle x in the following figure:

**(a)** 30°

**(b)** 35°

**(c)** 40°

**(d)** 45°

**Answer/Explanation**

Answer: (c)

Explanation : x + 90° = 130° ⇒ x = 40°.

**31.** Find the value of unknown x in the following figure:

**(a)** 40°

**(b)** 50°

**(c)** 45°

**(d)** 55°

**Answer/Explanation**

Answer: (b)

Explanation : x + 40° + 90° = 180° ⇒ x = 50°.

**32.** Find the value of unknown x in the following figure:

**(a)** 10°

**(b)** 15°

**(c)** 20°

**(d)** 25°

**Answer/Explanation**

Answer: (b)

Explanation : x + 5x + 90° = 180° ⇒ x = 15°.

**33.** Find angle x in the following figure:

**(a)** 90°

**(b)** 80°

**(c)** 95°

**(d)** 100°

**Answer/Explanation**

Answer: (a)

Explanation : x + 45 + 45° = 180° ⇒ x = 90°.

**34.** Find angle x in the following figure:

**(a)** 40°

**(b)** 50°

**(c)** 45°

**(d)** 60°

**Answer/Explanation**

Answer: (b)

Explanation : x = 50°.

**35.** Find angle x in the following figure:

**(a)** 40°

**(b)** 30°

**(c)** 25°

**(d)** 35°

**Answer/Explanation**

Answer: (b)

Explanation : x + x + 120° = 180° ⇒ x = 30°.

**36.** Find angle x in the following figure:

**(a)** 40°

**(b)** 45°

**(c)** 35°

**(d)** 50°

**Answer/Explanation**

Answer: (a)

Explanation : x + 140° = 180° ⇒ x = 40°.

**37.** Find angle x in the following figure:

**(a)** 58°

**(b)** 59°

**(c)** 57°

**(d)** 56°

**Answer/Explanation**

Answer: (a)

Explanation : x + x = 116° ⇒ x = 58°.

**38.** Find angle x in the following figure:

**(a)** 45°

**(b)** 40°

**(c)** 35°

**(d)** 50°

**Answer/Explanation**

Answer: (a)

Explanation : x = 45°.

**39.** In which case of the following lengths of sides of a triangle, is it possible to draw a triangle?

**(а)** 3 cm, 4 cm, 7 cm

**(b)** 2 cm, 3 cm, 7 cm

**(c)** 3 cm, 4 cm, 5 cm

**(d)** 3 cm, 3 cm, 7 cm

**Answer/Explanation**

Answer: (c)

Explanation : 3 + 4 > 5; 4 + 5 > 3; 5 + 3 > 4.

**40.** Which of the following cannot be the sides of a right triangle?

**(а)** 2 cm, 2 cm, 4 cm

**(b)** 5 cm, 12 cm, 13 cm

**(c)** 6 cm, 8 cm, 10 cm

**(d)** 3 cm, 4 cm, 5 cm

**Answer/Explanation**

Answer: (a)

Explanation : 22 + 22 = 8; 42 = 16

∴ 22 + 22 ≠ 42

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