Question

Chapter 8 The Triangle and its Properties
P
2. In APOR, A is a point on the side OR. Complete each of the statements
given below using symbol'','>'or'<' so as to make a true statement.
PA
PQ+QA
b. PA
PR+AR
PA
(PQ+OR+PR)
0
A
Special Triangles ID
Exploration Zone
obonom: We have learnt about properties of triangles in general. Now, let us learn the
properties of some special triangles, namely equilateral and isosceles triangles.
tredoc: Properties of 'Equilateral triangle' and 'Isosceles triangle'?​

Answer 1

Answer:

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

Explanation:

Solution:

(i) By angle sum property of a triangle, we have

∠x + 50° + 60° = 180°

⇒ ∠x + 110° = 180°

∴ ∠x = 180° – 110° = 70°

(ii) By angle sum property of a triangle, we have

∠x + 90° + 30 = 180° [∆ is right angled triangle]

⇒ ∠x + 120° = 180°

∴ ∠x – 180° – 120° = 60°

(iii) By angle sum property of a triangle, we have

∠x + 30° + 110° – 180°

⇒ ∠x + 140° = 180°

∴ ∠x = 180° – 140° = 40°

(iv) By angle sum property of a triangle, we have

∠x + ∠x + 50° = 180°

⇒ 2x + 50° = 180°

⇒ 2x = 180° – 50°

⇒ 2x = 130°

∴ x=13002=65∘

(v) By angle sum property of a triangle, we have

∠x + ∠x +∠x =180°

⇒ 3 ∠x = 180°

∴ ∠x=18003=60∘

(vi) By angle sum property of a triangle, we have

x + 2 x + 90° = 180° (∆ is right angled triangle)

⇒ 3x + 90° = 180°

⇒ 3x = 180° – 90°

⇒ 3x = 90°

∴ x=9003=30∘