Question

In the given figure (i), OP, OQ, OR and OS are four rays. I
ZPOQ + ZQOR + ZSOR + ZPOS = 360°​

Answer 1

Step-by-step explanation:

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Step-by-step explanation:

Given that

OP, OQ, OR and OS are four rays

You need to produce any of the ray OP, OQ, OR and OS backwards to a point in the figure. Let us produce ray OQ backwards to a point

T so that TOQ is a line

Ray OP stands on the TOQ

∠TOP + ∠POQ = 180° [Linear pair] ………...(1)

 

Similarly,

∠TOS + ∠SOQ = 180°  [Linear pair]  

∠TOS + (∠SOR + ∠OQR) = 180° ………. (2)

Adding eq (1) and (2), we obtain :

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

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

[∠TOP + ∠TOS = ∠POS]

∠POS + ∠POQ + ∠SOR + ∠QOR = 360°

Hence, ∠POQ + ∠QOR + ∠SOR + ∠POS = 360°

Answer 2

$\huge \underline{\pink{ \mathfrak{AnSwEr : }}} </p><p>$

Step-by-step explanation:

Given that

OP, OQ, OR and OS are four rays

You need to produce any of the ray OP, OQ, OR and OS backwards to a point in the figure. Let us produce ray OQ backwards to a point

T so that TOQ is a line

Ray OP stands on the TOQ

∠TOP + ∠POQ = 180° [Linear pair] ………...(1)

Similarly,

∠TOS + ∠SOQ = 180° [Linear pair]

∠TOS + (∠SOR + ∠OQR) = 180° ………. (2)

Adding eq (1) and (2), we obtain :

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

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

[∠TOP + ∠TOS = ∠POS]

∠POS + ∠POQ + ∠SOR + ∠QOR = 360°

Hence, ∠POQ + ∠QOR + ∠SOR + ∠POS = 360°