Question

In angle PQR, side QP has been extended and angle RPS = 130 degree. If Angle Q = 55 degree, find (i) angle QPR , (ii) Angle R​

Answer 1

Answer:

Given that:

QP=8cm,PR=6cm and SR=3cm

(I) In △PQR and △SPR

∠PRQ=∠SRP (Common angle)

∠QPR=∠PSR (Given that)

∠PQR=∠PSR (Properties of triangle )

∴△PQR∼△SPR (By AAA)

(II)

SP

PQ

=

PR

QR

=

SR

PR

(Properties of similar triangles)

⇒

SP

8cm

=

3cm

6cm

⇒SP=4cm and

⇒

6cm

QR

=

3cm

6cm

⇒QR=12cm

(III)

ar(△SPR)

ar(△PQR)

=

SP

2

PQ

2

=

4

2

8

2

=4

Answer 2

Answer: QPR = 50; R = 75

Step-by-step explanation:

SPR + QPR = 180 [ Linear Pair ]

130 + QPR = 180

QPR = 180 - 130

Thus, QPR = 50

P + Q + R = 180 [ Angle Sum Property ]

50 + 55 + R = 180

105 + R = 180

R = 180 - 105

Thus, R = 75