RD SHARMA Solutions for Class 9 Maths Chapter 11 - Triangle and its Angles
Chapter 11 - Triangle and its Angles Exercise 11.25
Question 1
If all the three angles of a triangle are equal, then each one of them is equal to
(a) 90°
(b) 45°
(c) 60°
(d) 30°
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).
Question 2
If two acute angles of a right triangle are equal, then each acute is equal to
(a) 30°
(b) 45°
(c) 60°
(d) 90°
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).
Question 3
An exterior angle of a triangle is equal to 100° and two interior opposite angle are equal. Each of these angles is equal to
(a) 75°
(b) 80°
(c) 40°
(d) 50°
Solution 3
Question 4
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
(a) an isosceles triangle
(b) an obtuse triangle
(c) an equilateral triangle
(d) a right triangle
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).
Question 5
Solution 5
Question 6
Solution 6
Question 7
In a triangle, an exterior angle at a vertex is 95° and its one of the interior opposite angle is 55°, then the measure of the other interior angle is
(a) 55°
(b) 85°
(c) 40°
(d) 9.0°
Solution 7
Question 8
If the sides of a triangle are produced in order, then the sum of the three exterior angles so formed is
(a) 90°
(b) 180°
(c) 270°
(d) 360°
Solution 8
Question 9
Solution 9
Question 10
An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of the triangle are
(a) 48°, 60°, 72°
(b) 50°, 60°, 70°
(c) 52°, 56°, 72°
(d) 42°, 60°, 76°
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Chapter 11 - Triangle and its Angles Exercise 11.26
Question 1
Solution 1
Question 2
In figure, x + y =
(a) 270°
(b) 230°
(c) 210°
(d) 190°
Solution 2
Question 3
If the measures of angles of a triangle are in the ratio of 3 : 4 : 5, what is the measure of the smallest angle of the triangle?
(a) 25°
(b) 30°
(c) 45°
(d) 60°
Solution 3
Question 4
Solution 4
Chapter 11 - Triangle and its Angles Exercise 11.27
Question 1
In figure, what is z in terms of x and y?
(a) x +y + 180°
(b) x + y - 180°
(c) 180° - (x + y)
(d) x + y + 360°
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
In figure, what is the value of x?
(a) 35
(b) 45
(c) 50
(d) 60
Solution 4
Chapter 11 - Triangle and its Angles Exercise 11.28
Question 1
In figure, the value of x is
(a) 65°
(b) 80°
(c) 95°
(d) 120°
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Chapter 11 - Triangle and its Angles Exercise 11.29
Question 1
If the bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is
(a) 45°
(b) 95°
(c) 135°
(d) 90°
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
Solution 6
Chapter 11 - Triangle and its Angles Exercise Ex. 11.1
Question 1
Solution 1
Question 2
Solution 2
Question 3
Solution 3
Question 4
Two angles of a triangle are equal and the third angle is greater than each of those angles by 30o. Determine all the angles of the triangle.
Solution 4
Question 5
Solution 5
Question 6
Can a triangle have:
(i) Two right angles?
(ii) Two obtuse angles?
(iii) Two acute angles?
(iv) All angles more than 60o?
(v) All angles less than 60o?
(vi) All angles equal to 60o?
Justify your answer in each case.
Solution 6
(i) No
As two right angles would sum up to 180o, and we know that the sum of all three angles of a triangle is 180o, 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 180o which is not possible as the sum of all three angles of a triangle is 180o.
(iii) Yes
A triangle can have 2 acute angles.
(iv) No
The sum of all the internal angles of a triangle is 180o. Having all angles more than 60o will make that sum more than 180o, which is impossible.
(v) No
The sum of all the internal angles of a triangle is 180o. Having all angles less than 60o will make that sum less than 180o, which is impossible.
(vi) Yes
The sum of all the internal angles of a triangle is 180o. So, a triangle can have all angles as 60o. Such triangles are called equilateral triangles.
Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10
Solution 10
Question 11
Solution 11
Question 12
Solution 12
Chapter 11 - Triangle and its Angles Exercise Ex. 11.2
Question 1
The exterior angles, obtained on producing both the base of a triangle both ways are 104o and 136o. Find all the angles of the triangle.
Solution 1
Question 2
In fig., the sides BC, CA and AB of a ΔABC have been produced to D, E, and F respectively. If ∠ACD = 105° and ∠EAF = 45°, find all the angles of the ΔABC.
Solution 2
Question 3
Solution 3
Question 4
Solution 4
Question 5
Solution 5
Question 6
In fig., AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD.
Solution 6
Question 7
In fig. AB ∥ DE. Find ∠ACD.
Solution 7
Question 8
Which of the following statements are true (T) and which are false (F):
Solution 8
Question 9
Fill in the blanks to make the following statements true:
(i) Sum of the angle of triangle is ______ .
(ii) An exterior angle of a triangle is equal to the two ______ opposite angles.
(iii) An exterior angle of a traingle is always _______ than either of the interior oppsite angles.
(iv) A traingle cannot have more than ______ right angles.
(v) A triangles cannot have more than ______ obtuse angles.
Solution 9
(i) 180o
(ii) interior
(iii) greater
(iv) one
(v) one
Question 10
Solution 10
Question 11
Solution 11
Question 12
In fig., AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine the value of x.
Solution 12
Question 13
Solution 13
Question 14
In fig., AM ⊥ BC and AN is the bisector of ∠A. If ∠B = 65° and ∠C = 33°, find ∠MAN.
Solution 14
Question 15
Solution 15
Question 16
Solution 16
Question 17
In fig. AE bisects ∠CAD and ∠B = ∠C. Prove that AE ∥ BC.
Solution 17
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