Question

3.find the value of x in each of the following diagrams:

Class_7th
Chapter_ triangles and its properties

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Answer 1

Answer:

x+2x = 105 (this is s property of triangle that external like this is equal to the sum of opposite two angles)

3x=105

x=35

Answer 2

There are 2 methods to solve this question.

First Method:

We know that sum of 2 angles on a straight line is 180°

This is known as 'Linear Pair of Angles'

Applying Linear Pair of angles,

∠ACB + ∠ACD = 180

⇒ ∠ACB + 105° = 180°

⇒ ∠ACB = 180° - 105°

⇒ ∠ACB = 75°

In ΔABC,

∠BAC + ∠ABC + ∠ACB = 180°

⇒ 2x + x + 75° = 180°                  [∵ ∠ACB = 75°]

⇒ 3x + 75° = 180°

⇒ 3x = 105°

⇒ x = 105 ÷ 3

∴ x = 35°

Second Method:

Applying Exterior Angle Property,

∠BAC + ∠ABC = ∠ACD

⇒ 2x + x = 105°

⇒ 3x = 105°

⇒ x = 105° ÷ 3

∴ x = 35°

Know More:

• What is Exterior Angle Property?

Exterior Angle Property states that the Exterior angle is equal to the sum of opposite interior angles.