Table of Contents
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(i)
Solution 3(i)
Question 3(ii)
Solution 3(ii)
Question 3(iii)
Solution 3(iii)
Question 4
In fig., AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD.
Solution 4
Question 5
In fig. AB ∥ DE. Find ∠ACD.
Solution 5
Question 6
Which of the following statements are true (T) and which are false (F):
Solution 6
Question 7
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 7
(i) 180o
(ii) interior
(iii) greater
(iv) one
(v) oneQuestion 8
Solution 8
Question 9
Solution 9
Question 10
In fig., AB divides ∠DAC in the ratio 1 : 3 and AB = DB. Determine the value of x.
Solution 10
Question 11
Solution 11
Question 12
In fig., AM ⊥ BC and AN is the bisector of ∠A. If ∠B = 65° and ∠C = 33°, find ∠MAN.
Solution 12
Question 13
Solution 13
Question 14
Solution 14
Question 15
In fig. AE bisects ∠CAD and ∠B = ∠C. Prove that AE ∥ BC.
Solution 15
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