PQ is the diameter of the circle with centre'O' . if <PQR=65°,<RPS=40°and <PQM=50°.find angle qpr angle prs and angle qpm plssss answer with steps
Answers
Answer:
(i) ∠QPR
∴ PQ is a diameter
∴ ∠PRQ = 90° [Angle in a semi-circle is 90°] In ΔPQR, ∠QPR + ∠PRQ + ∠PQR = 180° [Angle Sum Property of a triangle]
=> ∠QPR + 90° + 65°= 180°
=> ∠QPR + 155° = 180°
=> ∠QPR = 180° - 155°
=> ∠QPR = 25°
(ii) ∠PRS
∴ PQRS is a cyclic quadrilateral
∴ ∠PSR + ∠PQR = 180° [∴ Opposite angles of a cyclic quadrilateral are supplementary]
=> ∠PSR + 65° = 180°
=> ∠PSR = 180° - 65°
=> ∠PSR = 115°
In DPSR, ∠PSR + ∠SPR + ∠PRS = 180° [Angles Sum Property of a triangle]
=> 115° + 40° + ∠PRS = 180°
=> 115° + ∠PRS = 180°
=> ∠PRS = 180° - 155°
=> ∠PRS = 25°
(iii) ∠QPM
∴ PQ is a diameter
∴ ∠PMQ = 90° [∴ Angle in a semi - circle is 900] In ΔPMQ, ∠PMQ + ∠PQM + ∠QPM = 180° [Angle sum Property of a triangle]
=> 90° + 50° + ∠QPM = 180°
=> 140° + ∠QPM = 180°
=> ∠QPM = 180° - 140°
So angle QPM=40°
Step-by-step explanation:
ʜᴏᴘᴇ ᴛʜɪs ᴡɪʟʟ ʜᴇʟᴘ ᴜʜʜʜʜʜ☺☺
ғᴏʟʟᴏᴡ ᴍᴇ ᴘʟᴇᴀsᴇ