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Given $∠ P O R = 3 x$ and $∠ Q O R = 2 x + 10 ° .$ If $∠ P O Q$ is a straight line, then the

value of x is ____ °.

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Detailed Solution

Given

∠ P O R = 3 x

and

∠ Q O R = 2 x + 10 ° .

∠ P O Q

is a straight line, then the
value of x is 34 °.
Given a figure in which

∠ P O R = 3 x

and

∠ Q O R = 2 x + 10 °

Given POR = 3x and QOR = 2x + 10, find the value of x for which POQ will be a line(Fig).

As we know that, ∠POR and ∠QOR, form a linear pair,
Therefore, their sum will be supplementary.

∠ P O R + ∠ Q O R = 180 ∘

As,

∠ P O R = 3 x a n d ∠ Q O R = 2 x + 10

Putting the values,

⇒ 3 x + 2 x + 10 = 180 ⇒ 5 x + 10 = 180 ⇒ 5 x = 180 − 10 ⇒ 5 x = 170 ⇒ x = 1705 ⇒ x = 34

Hence, the value of x is 34°.

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