In Fig., OP, OQ, OR and OS are four rays, prove that:∠POQ + ∠QOR +

1.	In Fig., OP, OQ, OR and OS are four rays, prove that:∠POQ + ∠QOR + ∠SOR + ∠POS = 360°
Answer» Given that, OP, OQ, OR and OS are four rays You need to produce any of the rays OP, OQ, OR and OS backwards to a point T so that TOQ is a line. Ray OP stands on line TOQ ∠TOP + ∠POQ = 180°(Linear pair) (i) Similarly, ∠TOS + ∠SOQ =180°(ii) ∠TOS + ∠SOR + ∠OQR = 180°(iii) Adding (i) and (iii), we get ∠TOP + ∠POQ + ∠TOS + ∠SOR + ∠QOR = 360° ∠TOP + ∠TOS = ∠POS Therefore, ∠POQ + ∠QOR + ∠SOR +∠POS = 360°.

In Fig., OP, OQ, OR and OS are four rays, prove that:∠POQ + ∠QOR + ∠SOR + ∠POS = 360°

Answer»

Given that,

OP, OQ, OR and OS are four rays

You need to produce any of the rays OP, OQ, OR and OS backwards to a point T so that TOQ is a line.

Ray OP stands on line

TOQ ∠TOP + ∠POQ = 180°(Linear pair) (i)

Similarly,

∠TOS + ∠SOQ =180°(ii)

∠TOS + ∠SOR + ∠OQR = 180°(iii)

Adding (i) and (iii), we get

∠TOP + ∠POQ + ∠TOS + ∠SOR + ∠QOR = 360°

∠TOP + ∠TOS = ∠POS

Therefore,

∠POQ + ∠QOR + ∠SOR +∠POS = 360°.