NCERT solution class 7 chapter 6 The Triangle and its Properties exercise 6.3 mathematics

Exercise 6.3

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Introduction - Ex. 6.3, Triangle and its Properties - NCERT Class 7th Maths Solutions

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Q 1, Ex 6.3 - The Triangle and its Properties - Chapter 6 - Maths Class 7th - NCERT

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QUESTION 1 
Find the value of the unknown x in the following diagrams :

The sum of all interior angles of a triangle is 180°. By using this property, these problems can be
solved as follows.
(i) x + 50° + 60° = 180°
x + 110° = 180°
x = 180° -110°
x = 70°

(ii)  x + 90° + 30° = 180°
x + 120° = 180°
x = 180° - 120°
x = 60°

(iii) x + 30° + 110° = 180°
x + 140° = 180°
x = 180° - 140°
x = 40°

(iv) 50° + x + x = 180°
50° + 2x = 180°
2x = 180° - 50°
$x=\dfrac{130°}{2}=65°$

(v)  x + x + x = 180°
3x = 180° - 90°
$x=\dfrac{90}{3}=30°$

Q 2, Ex 6.3 - The Triangle and its Properties - Chapter 6 - Maths Class 7th - NCERT

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QUESTION 2 
Find the value of the unknowns x and y in the following diagrams:

Sol :
(i) y+ 120° = 180° (Linear pair)
y = 180° - 120°
y = 60°
x + y + 50° = 180° (Angle sum property)
x + 60° + 50° = 180°
x + 110° = 180°
x = 180° - 10°
x = 70°

(ii) y = 80° (Vertically opposite angles)
y + x + 50° = 180° (Angle sum property)
80° + x + 50° =180°
x + 130° = 180°
x = 180° - 130°
x = 50°

(iii) y + 50° +  60° = 180° (Angle sum property)
y = 180° - 60° - 50°
y = 70°
x +  y = 180° (Linear pair)
x = 180° - y
x = 180°-70°
x = 110°

(iv) x = 60° (Vertically opposite angles)
30° + x + y = 180°
30° + 60° + y = 180°
y = 180° - 30° - 60°
y = 90°

(v) y = 90° (Vertically opposite angles)
x + x + y = 180° (Angle sum property)
2x + y = 180°
2x + 90° = 180°
2x = 180° - 90°
$x=dfrac{90°}{2}=45°$

(vi)

y = x ( Vertically opposite angles )
a = x ( Vertically opposite angles )
b = x ( Vertically opposite angles )
a + b+ y=180° (Angle sum property)
x + x + x = 180°
3x = 180°
$x=\dfrac{180°}{3}=60°$
y = x = 60°