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

(Below fig).

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#### Solution

Since `∠`*QOR*, `∠`*POP *are linear pairs

*`∠`QOR *+ `∠`*POR *= 180°

2*x *+10 + 3*x *= 180° [ ∴ `∠`*QOR *= 2*x *+10, `∠`*POR *= 3*x*]

*⇒ *5*x *+10 = 180°

*⇒ *5*x *= 180° -10

*⇒* 5*x *= 170°

*⇒ x *= 34°

Concept: Pairs of Angles

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