Question

find x......................​

Answer 1

Answer:

The value of x is $\tt {70°}$.

Step-by-step explanation-

$</u><u>∠a = 180° - x</u><u>$

$</u><u> </u><u>∠b = 360° - 3x</u><u>$

$</u><u> </u><u>∠c = 180° - 2x</u><u>$

We know that the sum of the angles of a quadrilateral is 360°.

$∴ \: ∠a + ∠b \: + \: ∠c \: + 60° = 360°$

$⇒180° - x + 360° - 3x + 180° - 2x + 60°= 360°$

Now, collect all like terms and solve the equation.

$⇒ - x - 3x - 2x + 180° + 180° + 360°+ 60°= 360°$

$⇒ - 6x + 780° = 360°$

$⇒ - 6x = 360° - 780°$

$⇒ - 6x = - 420°$

$∴x = \frac{-420°}{-6} = 70°$

Hence, x = 70°

Answer 2

Answer:-

Given:-

• ∠a = 180° - x
• ∠b = 360° - 3x

[∵ ∠b + 3x = 360° (Reflex)]

• ∠c = 180° - 2x
• Constant angle given = 60°

To Find:-

Measurement of x in the given figure.

_____________...

We know,

Sum of int. ∠s of a quadrilateral = 360°

According to the Question:-

∠a + ∠b + ∠c + 60° = 360°

After substitution of the angles... (see Given)

⟹ (180° - x) + (360° - 3x) + (180° - 2x) + 60° = 360°

⟹ 180° - x + 360° - 3x + 180° - 2x + 60° = 360°

⟹ 180° + 360° + 180° + 60° - x - 3x - 2x = 360°

⟹ 780° - 6x = 360°

⟹ - 6x = 360° - 780°

⟹ - 6x = - 420°

⟹ 6x = 420°

⟹ x = 420°/6

⟹ x = 70° ...(Answer)

Verification:- (Not Required)

LHS:-

(180° - x) + (360° - 3x) + (180° - 2x) + 60°

= (180° - 70°) + [360° - 3(70°)] + [180° - 2(70°)] + 60°

= 110° + (360° - 210°) + (180° - 140°) + 60°

= 110° + 150° + 40° + 60°

= 260° + 100°

= 360°

RHS:-

360°

∴ LHS = RHS.