Question

in fig, lines /_PQR=/_PRQ , then prove that/_PQS=/_PRT.​

Answer 1

Answer:

LET

/_ PQR= x /_ PRQ=y. /_PQS=a /_ PRT=b

proof,

x=y (given)

x+a=180 ( linear pairs)

a=180-x........1

y+b=180 ( linear pairs)

b=180-y

b=180-x (x=y given).....2

from 1 and 2 ,we get,

a=b

that is/_ PQS=/_PRT

hope it helps

Answer 2

Answer:

We can prove

Step-by-step explanation:

We can solve this problem by using linear pair angles i.e.,

sum of two adj. angles are equal to 90 degrees

here in this figure there are 2 linear pair angles

Those are (∠PQS, ∠PQR) , (∠PRQ, ∠PRT)

From linear pair angles we can say that

∠PQS + ∠PQR = ∠PRT + ∠PRQ { ∵ Both sum = 90°}

∠PQS + ∠PQR = ∠PRT + ∠PQR { ∵ Given In The Question}

∠PQS + ∠PQR - ∠PQR = ∠PRT

∠PQS = ∠PRT

HENCE PROVED

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