# Class 9 RD SHARMA Solutions Maths Chapter 11 - Triangle and its Angles

## Triangle and its Angles Exercise Ex. 11.1

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(i) No

As two right angles would sum up to 180^{o}, and we know that the sum of all three angles of a triangle is 180^{o}, so the third angle will become zero. This is not possible, so a triangle cannot have two right angles.

(ii) No

A triangle cannot have 2 obtuse angles, since then the sum of those two angles will be greater than 180^{o }which is not possible as the sum of all three angles of a triangle is 180^{o}.

(iii) Yes

A triangle can have 2 acute angles.

(iv) No

The sum of all the internal angles of a triangle is 180^{o}. Having all angles more than 60^{o} will make that sum more than 180^{o}, which is impossible.

(v) No

The sum of all the internal angles of a triangle is 180^{o}. Having all angles less than 60^{o} will make that sum less than 180^{o}, which is impossible.

(vi) Yes

The sum of all the internal angles of a triangle is 180^{o}. So, a triangle can have all angles as 60^{o}. Such triangles are called equilateral triangles.

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## Triangle and its Angles Exercise Ex. 11.2

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(i) 180^{o}

(ii) interior

(iii) greater

(iv) one

(v) one

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## Triangle and its Angles Exercise 11.25

### Solution 1

Let the measure of each angle be x°.

Now, the sum of all angles of any triangle is 180°.

Thus, x° + x° + x° = 180°

i.e. 3x° = 180°

i.e. x° = 60°

Hence, correct option is (c).

### Solution 2

Let the measure of each acute angle of a triangle be x°.

Then, we have

x° + x° + 90° = 180°

i.e. 2x° = 90°

i.e. x° = 45°

Hence, correct option is (b).

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### Solution 4

Let the three angles of a triangle be A, B and C.

Now, A + B + C = 180°

If A = B + C

Then A + (A) = 180°

i.e. 2A = 180°

i.e. A = 90°

Since, one of the angle is 90°, the triangle is a Right triangle.

Hence, correct option is (d).

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## Triangle and its Angles Exercise 11.26

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## Triangle and its Angles Exercise 11.27

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## Triangle and its Angles Exercise 11.28

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## Triangle and its Angles Exercise 11.29

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