Question

In the above figure PQS =SRQ, QPR=SQR. U is a point on qr such that QPU =30 .then QUP is​

Answer 1

Step-by-step explanation:

Here,

∠PQS=∠SRQ, ∠QPR=∠SQR and ∠QPU=30°

Then,

∠PQR+∠PRQ+∠QPR=180°(sum of interior angles of a triangle is 180°)

or, ∠PQS+∠SQR+∠SRQ+∠SQR=180(since ∠PQR=∠PQS+∠SQR and ∠PRQ=∠SRQ)

or, ∠SRQ+∠SQR+∠SRQ+∠SQR=180°

or, 2∠SRQ+2∠SQR=180°

or, 2(∠SRQ+∠SQR) =180°

or, (∠SRQ+∠SQR) = 90°

i.e. (∠PQS+∠SQR) = 90° (since ∠PQS and ∠SRQ are same)

i.e. ∠PQR= 90° (∠PQR=∠PQS+∠SQR)

Now,

∠PQU+∠QUP+∠QPU=180°(sum of interior angles of a triangle is 180°)

or, ∠PQR+∠QUP+30°=180° (∠PQU and ∠PQR are same)

or, 90°+ ∠QUP+30°=180°

or, 120+∠QUP=180°

or, ∠QUP=180°-120°

i.e. ∠QUP=60°