Question

Pqr is a triangle in which rs is perpendicular to pq and qt is is perpendicular to pr.Rs and qt intersect at o prove that angle qor =180 - angle p

Answer 1

Answer:

∠QOR = 180° - ∠P

Step-by-step explanation:

Pqr is a triangle in which rs is perpendicular to pq and qt is is perpendicular to pr.Rs and qt intersect at o prove that angle qor =180 - angle p

in Δ ORT

∠ROT  + 90° +  ∠TRO = 180°

=> ∠ROT = 90° -  ∠TRO  eq 1

in  Δ  PRS

∠PRS + 90° + ∠P = 180°

=> ∠PRS = 90° - ∠P

∠PRS = ∠TRO as T lies on PR & O lies on RS

=> ∠TRO  = 90° - ∠P

putting this in eq 1

=>  ∠ROT = 90° - (90° - ∠P)

=> ∠ROT = ∠P

∠ROT + ∠QOR = 180°  ( straight line)

=> ∠P + ∠QOR = 180°

=> ∠QOR = 180° - ∠P

Answer 2

Refer to the attachment above.