Question

in below fig OP, OQ, OR and OS are four rays prove that
POQ + LQOR + LSOR + LPOS= 360°​

Answer 1

Solution:

Produce ray OQ backwards to a point T so that TOQ is a line. (2nd diagram)

Now, ray OP stands on line TOQ.

Therefore,

∠TOP + ∠POQ = 180° ----(1) (Linear Pair)

Similarly, ray OS stands on line TOQ.

Therefore,

∠TOS + ∠SOQ = 180° ----(2)

But,

∠SOQ = ∠SOR + ∠QOR

So, (2) becomes

∠TOS + ∠SOR + ∠QOR = 180° -----(3)

Now, adding (1) and (3), we get,

∠TOP + ∠POQ + ∠TOS + ∠SOR + ∠QOR = 360°-----(4)

But,

∠TOP + ∠TOS = ∠POS

Therefore, (4) becomes

∠POQ + ∠QOR + ∠SOR + ∠POS = 360°

Answer 2

Answer:

reffer to the attached photo....

minatian~