The DAV Class 5 Maths Solutions and **DAV Class 5 Maths Chapter 16 Worksheet 2** Solutions of Triangles offer comprehensive answers to textbook questions.

## DAV Class 5 Maths Ch 16 Worksheet 2 Solutions

Question 1.

Measure the angles of the triangle given below. What is the sum of the three angles?

Solution:

∠X = 50°

∠Y = 60°

∠Z = 70°

∠X + ∠Y + ∠Z = 50° + 60° + 70° = 180°

Question 2.

Find which of the following can be the measures of three angles of a triangle.

(a) 35°, 80°, 65°

Solution:

35°+ 80°+ 65° = 180°

Yes (The sum of angles of the triangle is 180°)

(b) 15°, 75°, 90°

Solution:

15° + 75° + 90° = 180°

Yes (The sum of angles of the triangle is 180°)

(c) 70°, 70°, 70°

Solution:

70° + 70° + 70° = 210°

No (The sum of the angles of the triangle is 180°)

(d) 45°, 59°, 81°

Solution:

45° + 59° + 81° = 185°

No (The sum of angles of a triangle is 180°)

Question 3.

Can you draw a triangle with two right angles? Give reasons.

Solution:

No, because the sum of 3 angles of a triangle will not be equal to 180°.

Question 4.

Can you draw a triangle with two obtuse angles? Give reasons.

Solution:

No, because the sum of 3 angles will exceed 180° so drawing a triangle is not possible with two obtuse angles.

Question 5.

Find the missing angle in each of the following:

(a)

Solution:

The sum of 3 angles of the triangle is 180°

So let the missing angle be x°.

x° + 65° + 40° = 180°

⇒ x° + 105° = 180°

⇒ x° = 180° – 105°

⇒ x° = 75°

(b)

Solution:

The sum of 3 angles of the triangle is 180°

Let the missing angle be x°.

x° + 90° + 47° = 180°

⇒ x° + 137° = 180°

⇒ x° = 180° – 137°

⇒ x° = 43°

(c)

Solution:

Let the missing angle be x°

40° + x° + 40° = 180° (Sum of angles of triangle is 180°)

⇒ 80° + x° = 180°

⇒ x° = 180° – 80°

⇒ x° = 100°

Question 6.

The sum of two angles of a triangle is 110°. Find the measure of the third angle.

Solution:

Let the third angle be x°.

Sum of two angles + third angle = 180°

⇒ 110° + x° = 180°

⇒ x° = 180° – 110°

⇒ x° = 70°

Question 7.

Two angles of a triangle are 100° and 55° respectively. Find the third angle.

Solution:

Two angles are 100° and 55°.

Let the third angle be x°.

So 100° + 55° + x° = 180° (sum of angle of triangle is 180°)

⇒ 155° + x° = 180°

⇒ x° = 180° – 155°

⇒ x° = 25°

**DAV Class 5 Maths Chapter 16 Worksheet 2 Notes**

**Properties of a Triangle**

Property I:

The sum of the measures of the three angles of a triangle is always 180°.

Explanation:

∠A + ∠B + ∠C = 60° + 50° + 70° = 180°

Example 1.

Find out the third angle of a triangle when the other two angles are given.

∠A = 55°

∠B = 30°

Find the ∠C =?

Solution:

Sum of angles = 180°

So, ∠A + ∠B + ∠C = 180°

⇒ 55° + 30° + ∠C = 180°

⇒ 85° + ∠C = 180°

⇒ ∠C = 180° – 85° = 95°

So the third angle is 95°.

Property II:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Explanation:

AB = 4 cm

AC = 3 cm

BC = 5 cm

AB + BC = 9 cm

9 is greater than 3 or BC + AC = 8 cm

AB = 4 cm

8 is greater than 4 or AB + AC = 7 cm

BC = 5 cm

7 is greater than 5

So we observe that the sum of any two sides of a triangle is always greater than the third side.

Example 2.

Can we draw a triangle with line segments of lengths 2 cm, 3 cm, and 8 cm?

Solution:

Length of first side = 2 cm

Length of second side = 3 cm

Length of third side = 8 cm

Sum of first and second side = 2 cm + 3 cm = 5 cm

Length of third side = 8 cm

8 > 5 or 5 < 8

So, we cannot draw a triangle with the line segments.