Selina Solutions Concise Mathematics Class 6 Chapter 26 Triangles Exercise 26(A) consists of problems on determining the angle of the given set of triangles. A triangle is defined as a closed figure which has three sides and vertices. The main objective of preparing exercise wise solutions is to develop a strong foundation of fundamental concepts discussed under this exercise. These concepts are vital as it will be continued in higher class as well. In order to obtain a clear conceptual knowledge, students can access Selina Solutions Concise Mathematics Class 6 Chapter 26 Triangles Exercise 26(A) PDF, from the links which are provided here
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Exercise 26(A)
1. In each of the following, find the marked unknown angles:
Solution:
(i) We know that,
Sum of all angles of triangle = 1800
Therefore,
700 + 720 + z = 1800
1420 + z = 1800
z = 1800 – 1420
We get,
z = 380
(ii) We know that,
Sum of all angles of a triangle = 1800
First triangle
500 + 800 + b = 1800
1300 + b = 1800
b = 1800 – 1300
We get,
b = 500
Second triangle
400 + 450 + a = 1800
850 + a = 1800
a = 1800 – 850
We get,
a = 950
(iii) 600 + 450 + 200 + x = 1800
1250 + x = 1800
x = 1800 – 1250
We get,
x = 550
2. Can a triangle together have the following angles?
(i) 550, 550 and 800
(ii) 330, 740 and 730
(iii) 850, 950 and 220
Solution:
(i) Sum of all angles of a triangle = 1800
Here,
550 + 550 + 800 = 1800
We get,
1900 ≠1800
Therefore, it cannot form a triangle
(ii) 330 + 740 + 730 = 1800
We get,
1800 = 1800
Therefore, it form a triangle
(iii) 850 + 950 + 220 = 1800
We get,
2020 ≠1800
Therefore, it cannot form a triangle
3. Find x, if the angles of a triangle are:
(i) x0, x0, x0
(ii) x0, 2x0, 2x0
(iii) 2x0, 4x0, 6x0
Solution:
We know that,
The sum of all the angles in a triangle is 1800
So,
x0 + x0 + x0 = 1800
3x = 1800
x = 1800 / 3
We get,
x = 600
The value of x = 600
(ii) We know that,
The sum of all the angles in a triangle is 1800
So,
x + 2x + 2x = 1800
5x = 1800
x = 1800 / 5
We get,
x = 360
Therefore, the value of x = 360
(iii) We know that,
The sum of all the angles in a triangle is 1800
So,
2x + 4x + 6x = 1800
12x = 1800
x = 1800 / 12
We get,
x = 150
Therefore, the value of x = 150
4. One angle of a right-angled triangle is 700. Find the other acute angle.
Solution:
We know that,
Sum of all the angles in a triangle = 1800
Let us consider the acute angle as x
Hence,
x + 900 + 700 = 1800
x + 1600 = 1800
x = 1800 – 1600
We get,
x = 200
Therefore, the acute angle is 200
5. In △ABC, ∠A = ∠B = 620; find ∠C
Solution:
Given
∠A = ∠B = 620
So,
∠A + ∠B + ∠C = 1800
620 + 620 + ∠C = 1800
1240 + ∠C = 1800
∠C = 1800 – 1240
We get,
∠C = 560
Hence, ∠C = 560
6. In △ABC, ∠B = ∠C and ∠A = 1000; find ∠B.
Solution:
Given
∠B = ∠C
We know that,
Sum of all the angles in a triangle is 1800
∠A + ∠B + ∠C = 1800
1000 + ∠B + ∠B = 1800
1000 + 2∠B = 1800
2∠B = 1800 – 1000
We get,
2∠B = 800
∠B = 800 / 2
∠B = 400
Therefore, ∠B + ∠C = 400
7. Find, giving reasons, the unknown marked angles, in each triangle drawn below:
Solution:
We know that,
Exterior angle of a triangle is always equal to the sum of its two interior opposite angles (property)
So,
(i) 1100 = x + 300 [By property]
x = 1100 – 300
We get,
x = 800
(ii) x + 1150 = 1800 [By linear property of angles]
x = 1800 – 1150
We get,
x = 650
By exterior angle property
x + y = 1150
650 + y = 1150
y = 1150 – 650
We get,
y = 500
Therefore the value of angle x is 650 and y is 500
(iii) By exterior angle property,
1100 = 2x + 3x
5x = 1100
x = 1100 / 5
We get,
x = 220
Hence,
The value of 2x = 2 × 22
= 440
The value of 3x = 3 × 22
= 660
8. Classify the following triangles according to angle:
Solution:
(i) Since, one of the angle of a triangle is 1200.
Therefore, it is obtuse angled triangle
(ii) Since, all the angles of a triangle is less than 900
Therefore, it is acute angled triangle
(iii) Since ∠MNL = 900 and
Sum of two acute angle s,
∠M + ∠N = 300 + 600
= 900
Therefore, it is right angled triangle
9. Classify the following triangles according to sides:
(i)
(ii)
Solution:
(i) In the given triangle, we find two sides are equal.
Therefore, it is isosceles triangle
(ii) In the given triangle, all the three sides are unequal.
Therefore, it is scalene triangle
(iii) In the given triangle, all the three sides are unequal.
Therefore, it is scalene triangle
(iv) In the given triangle, all the three sides are equal.
Therefore, it is equilateral triangle
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