Question

in a triangle pqr ,s is the mid point of PR such QS = 1/2PR then angle PQR is​

Answer 1

Given :-

• S is mid point of PR .
• QS = (1/2) PR .

To Find :-

• ∠PQR = ?

Solution :-

Given that,

→ S is mid point of PR .

So,

→ PS = SR = (1/2) PR .

also,

→ QS = (1/2) PR .

then,

→ PS = SR = QS .

now, In ∆QSR we have,

→ QS = SR .

so,

→ ∠SQR = ∠SRQ = Let x . (Angle Opp. to Equal sides are Equal.)

now, in ∆PQS we have,

→ PS = SQ

So,

→ ∠QPS = ∠PQS = Let y . (Angle Opp. to Equal sides are Equal.)

Now, in ∆PQR , we have ,

→ ∠PRQ + ∠PQR + ∠QPR = 180° .(Angle sum Property.)

→ x + (x + y) + y = 180°

→ 2x + 2y = 180°

→ 2(x + y) = 180°

Dividing both sides by 2,

→ (x + y) = 90°.

therefore,

→ ∠PQR = (x + y) = 90° (Ans.)

Hence, angle PQR is equal to 90° .

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