Question

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

Answer 1

Since `∠`QOR, `∠`POP are linear pairs

`∠`QOR + `∠`POR = 180°

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

⇒ 5x +10 = 180°

⇒ 5x = 180° -10

⇒ 5x = 170°

⇒ x = 34°