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Find the value of the unknown x in the following diagrams:
Find the value of the unknown x in the following diagrams

Solution:

We make use of the angle sum property of a triangle according to which the sum of the interior angles of a triangle is always equal to 180°.

(i) Sum of interior angles of a triangle = 180°

∠𝐴 + ∠𝐵 + ∠𝐶 = 180°

𝑥 + 50° + 60° = 180°

𝑥 = 180° − 110° = 70°

(ii) Sum of interior angles of a triangle = 180°

∠𝑃 + ∠𝑄 + ∠𝑅 = 180°

90° + 30° + 𝑥 = 180°(∠P = 90° from figure)

𝑥 = 180° − 120° = 60°

(iii) Sum of interior angles of a triangle = 180°

∠𝑋 + ∠𝑌 + ∠𝑍 = 180°

30° + 110° + 𝑥 = 180°

𝑥 = 180° − 140° = 40°

(iv) Sum of interior angles of a triangle = 180° 𝑥 + 𝑥 + 50° = 180°

2 𝑥 + 50° = 180°

2𝑥 = 180° − 50°

x = 130° /2 = 65°

(v) Sum of interior angles of a triangle = 180° 

𝑥 + 𝑥 + 𝑥 = 180°

3𝑥 = 180°

x = 180° /3 = 60°

(vi) Sum of interior angles of a triangle = 180° 

𝑥 + 2𝑥 + 90° = 180°

3𝑥 + 90° = 180°

3𝑥 = 180° − 90

x = 90°/3 = 30°

☛ Check: NCERT Solutions Class 7 Maths Chapter 6

Video Solution:

Find the value of the unknown x in the following diagrams:
 

NCERT Solutions for Class 7 Maths Chapter 6 Exercise 6.3 Question 1

Summary:

The value of the unknown x in the following diagrams are: (i) x = 70°, (ii) 𝑥 = 60°, (iii) x =  40°, (iv) x = 65°, (v) x = 60°, (vi) x =  30°

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