Question

Find x in the follor
given triangle​

Answer 1

Answer :

• The value of x = 36°.

Given :-

• The angles of the triangle are (2x - 40)°, (3x - 80)° and (5x - 60)°.

To find :-

• The value of x.

Step-by-step explanation :-

We know the value of the angles in the triangle.

The sum of all the angles in a triangle = 180°.

Thus, we get :-

$\sf(2x - 40)^{\circ} + (3x - 80)^{\circ} + (5x - 60)^{\circ} = 180^{\circ}.$

On removing the brackets,

$\sf2x^{\circ} + (- 40)^{\circ} + 3x^{\circ} + (- 80)^{\circ} + 5x^{\circ} + ( - 60)^{\circ} = 180^{\circ}$

On putting the constants and variables separately,

$\sf2x^{\circ} + 3x^{\circ} + 5x^{\circ} + ( - 40)^{\circ} + (- 80)^{\circ} + (- 60)^{\circ} = 180^{\circ}$

On simplifying,

$\sf10x^{\circ} + ( - 180)^{\circ} = 180^{\circ}$

(+) and (-) = (-), so :-

$\sf10x^{\circ} - 180^{\circ} = 180^{\circ}$

Transposing 180 from LHS to RHS, changing its sign,

$\sf10x^{\circ} = 180^{\circ} + 180^{\circ}$

On simplifying,

$\sf10x^{\circ} = 360^{\circ}$

Transposing 10 from LHS to RHS, changing its sign,

$\sf x = \dfrac{360^{\circ}}{10^{\circ}}$

Dividing 360 by 10,

$\sf x = 36^{\circ}.$

Therefore, x = 36°.

Therefore, the value of each angle :-

(2x - 40)° = (2 × 36° - 40°) = 32°.

(3x - 80)° = (3 × 36 - 80°) = 28°.

(5x - 60)° = (5 × 36° - 60°) = 120°.

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Verification :-

(Optional)

To check our answer, we just have to put 36 (value of x) in place of x and check whether the LHS = RHS.

We can also check by adding the value of all the angles and see whether we get 180° or not (The sum of all the angles in a triangle).

32° + 28° + 120° = 180°.

Since the sum of all the angles is 180°,

Hence verified! ✔️✔️

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