Question

In the given figure, AOB is a straight line. find the value of x​

Answer 1

Answer :-

• The value of x is 32°.

Given :-

• AOB is a straight line.

To find :-

• The value of x.

Step-by-step explanation :-

• In the given figure, we can see that AOB is a straight line, we have to find the value of x. Let's do it by using a special property of lines and angles.

We know that :-

$\boxed{\sf Sum \: of \: angles \: on \: a \: straight \: line = 180^{\circ}.}$

• It means that all these angles must add up to 180°.

$\tt\Rightarrow(3x - 8)^{\circ} + 50^{\circ} + (x + 10)^{\circ} = 180^{\circ}$

Removing the brackets,

$\tt\Rightarrow3x - 8^{\circ} + 50^{\circ} + x + 10^{\circ} = 180^{\circ}$

Putting the constants and variables separately,

$\tt\Rightarrow3x + x - 8^{\circ} + 50^{\circ} + 10^{\circ} = 180^{\circ}$

On simplifying,

$\tt\Rightarrow4x - 8^{\circ} + 50^{\circ} + 10^{\circ} = 180^{\circ}$

On adding all the numbers,

$\tt\Rightarrow4x + 52^{\circ} = 180^{\circ}$

Transposing 52° from LHS to RHS, changing it's sign,

$\tt\Rightarrow4x = 180^{\circ} - 52^{\circ}$

On simplifying,

$\tt\Rightarrow4x = 128^{\circ}$

Transposing 4 from LHS to RHS, changing it's sign,

$\tt\Rightarrow x = \dfrac{128^{\circ}}{4}$

Dividing 128° by 4,

$\tt\Rightarrow x = 32^{\circ}$

• Hence, the value of x is 32°.

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Know more :-

All the angles are as follows :-

$\sf3x - 8^{\circ} = 3 \times 32^{\circ} - 8^{\circ} = 96^{\circ} - 8^{\circ} = 88^{\circ}$

$\sf50^{\circ} = 50^{\circ}$

$\sf x + 10^{\circ} = 32^{\circ} + 10^{\circ} = 42^{\circ}$

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