Haryana State Board HBSE 7th Class Maths Solutions Chapter 6 The Triangles and Its Properties Ex 6.3 Textbook Exercise Questions and Answers.
Haryana Board 7th Class Maths Solutions Chapter 6 The Triangles and Its Properties Exercise 6.3
Question 1.
Find the value of the unknown x in the following diagrams :
Solution:
By angle – sum’property of triangle,
(i) ∠A + ∠B + ∠C = 180°
or, x° + 50° + 60° = 180°
or, x° + 110 = 180°
or, x° = 180°-110°
∴ x° = 70°.
(ii) ∠P + ∠Q + ∠R = 180°
or, 90° + 30° + x° = 1800
or, 120 + x° = 180°.
∴ x° = 180° -120° = 60°.
(iii) ∠X + ∠Y + ∠Z = 180°
or, 30° + 110° + x° = 180°
or, 140 + x° = 180°.
∴ x° = 180°-140° = 40°
(iv) y x° +x° + 50° = 180°
or, 2x°+ 50° = 180°
or, 2x° = 180° – 50° = 130°
∴ x° = \(\frac{130}{2}\) = 65°
(v) x° + x° + x° = 180°
or, 3x° = 180°
∴ x° = \(\frac{180}{3}\) = 60°.
(vi) x° + 2x° + 90° 180°
or, 3x° = 180°-90° = 90°
∴ x° = \(\frac{90}{3}\) = 30°. 3
Question 2.
Find the values of the unknowns x and y in the following diagrams:
Solution:
By angle – sum property of a triangle the three angles of a triangle have a total measure of 180°.
The external angle of a triangle is equal to the sum of of its interior opposite angles and the linear pair = 180°.
(i) x° + 50° = 120°
x° = 120°-50° = 70°
Now, x° + y° + 30° = 180°
or, 70° + y° + 30° = 180°
or y° = 180°-70° = 30°
= 180° -100° = 80°.
x° = 70° , y° = 80°.
ii) y° = 80° vertically opposite angles
Now, x° + y° + 50° = 180°
or, x° + 80° + 50° = 180°
or, x° + 130° = 180°
∴ x° = 180° -130° = 50°
∴ x° = 50°, y° = 80°.
(iii) x° = 50° + 60° = 110°
or, y° + 50° + 60° = 180°
or, y° + 110° = 180°
∴ y°= 180° -110° = 70°
∴ x° = 110°, y° = 70°.
(iv) x° = 60° = vertically opposite angles
Now, x°+y° + 30° = 180°
60° +y° + 30° = 180°
y° + 90° = 180°
∴ y° = 180°-90° = 90°
∴ x° = 60°, y° = 90°.
(v) y° = 90° = = vertically opposite angle
Now, x° + x° +y° = 180°
or, 2x°+ 90° = 180°
or, 2x° = 180°-90° = 90°
∴ x° = \(\frac{90}{2}\) = 45°
∴ angle are, 45°, 45°, 90°.
(vi) x° = x° = vertically opposite angles
Now, x° = y° = vertically opposite angles
∴ x° + x° + x° = 180°
or, 3x° = 180°
∴ x° = \(\frac{180}{3}\) = 60°
∴ x° = 60°,
∴ x° = 60°,
y° = 60°.