Question

find x if the angle of the triangle are 2x,4xand 6x​

Answer 1

Given :

• Angles of triangle :-
• 2x, 4x and 6x

To find :

• The value of x

Knowledge required :-

• Formula for calculating sum of interior angles of a polygon :-

Sum of interior angles of polygon =

⠀⠀⠀⠀(2n - 4) × 90°

Where,

• n is the number of sides.

Solution :

A triangle has 3 sides, 3 angles.

So,

• n = 3

⠀⠀⠀⇒ 2x + 4x + 6x = (2n - 4) × 90°

⠀⠀⠀⇒ 12x = ((2 × 3) - 4) × 90°

⠀⠀⠀⇒ 12x = (6 - 4) × 90°

⠀⠀⠀⇒ 12x = 2 × 90°

⠀⠀⠀⇒ 12x = 180°

⠀⠀⠀⇒ x = 180°/12

⠀⠀⠀⇒ x = 90°/6

⠀⠀⠀⇒ x = 45°/3

⠀⠀⠀⇒ x = 15°

∴ The value of x = 15°

• First angle = 2x = 2 × 15° = 30°
• Second angle = 4x = 4 × 15° = 60°
• Third angle = 6x = 6 × 15° = 90°

━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀Verification :

To verify, add all the angles of triangle if their sum is equal to 180° then the value of x is right.

⠀⠀⠀⇒ 30° + 60° + 90°

⠀⠀⠀⇒ 180°

Sum of angles of triangle = 180°

Hence, verified.

Answer 2

$\huge \bold \purple{solution}$

=>. First angle of triangle ∆ = 2x

Second angle of triangle ∆ = 4x

Third angle of triangle ∆ = 6x

=>. 2x + 4x + 6x = 180 [Angle sum property]

=>. 12x = 180

=>. x = 180/12

=>. x = 15

Hence, first angle = 2x = 2×15 = 30

Second angle = 4x = 4×15 = 60

Third angle = 6x = 6×15 = 90

Hope it's help you.........................

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