Question

In the given figure , angle 1=2x-10°and angle 2 =3x+20°, find x and hence angle 1 and angle 2 ​

Answer 1

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Answer 2

$\Large\sf\underbrace{Question:-}$

In the given figure , angle 1=2x-10°and angle 2 =3x+20°, find x and hence angle 1 and angle 2

$\sf\Large{\underline{\underline{Answer:-}}}$

Find:-

• The value of x and ∠1 and ∠2.

Given,

• ∠1 = 2x - 10°

• ∠2 = 3x + 20°

We know that,

The ∠BOA and ∠AOC is forming a linear pair which measures 180°.

So,

$\Longrightarrow$ ∠1 + ∠2 = 180° [linear pairs]

$\Longrightarrow$ (2x - 10°) + (3x + 20°) = 180°

• Distribute the like terms,

$\Longrightarrow$ 2x + 3x - 10 + 20 = 180°

$\Longrightarrow$5x + 10 = 180°

$\Longrightarrow$5x = 180° - 10°

$\Longrightarrow$5x = 170°

$\Longrightarrow$x = $\sf{\cancel\dfrac{170}{5}}$

➥ x = 34°

∴ The value of x is 34°

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Now,

∠1 = 2x - 10°

∠1 = 2(34°) - 10°

∠1 = 68° - 10°

➥∠1 = 58°

Also,

∠2 = 3x + 20°

∠2 = 3(34°) + 20°

∠2 = 102° + 20°

➥∠2 = 122°

∴ The value of ∠1 is 58° and value of ∠2 is 122°.

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