in a quadrilateral pqrs ,the bisectors of angle R and angle S meet at point T.

Prove that angle P+ angle Q= 2angle RTS

Question

in a quadrilateral pqrs ,the bisectors of angle R and angle S
meet at point T
Prove that angle P+ angle Q= 2angle RTS

Ashutosh Verma · Accepted Answer

Answer: We have a quadrilateral PQRS , where bisectors of angle R and angle S meet at point T

We know in quadrilateral, ∠ P + ∠Q + ∠R + ∠S = 360° ∠ P + ∠Q = 360° - (∠R + ∠S) --------------- (1) In ∆RTS , ∠RTS + ∠TSR + ∠SRT = 180° --------------- (2) Given, ∠TSR = ∠S2 ∠SRT = ∠R2 After substitute this in equation (2) , we get ∠RTS + ∠S2 +∠R2 = 180° ⇒ 2∠RTS +∠S +∠R = 360° ⇒ 2∠RTS = 360° - (∠R + ∠S) From equation number (1) ⇒ 2∠RTS = ∠ P + ∠Q (Hence proved) Answer: We have a quadrilateral PQRS , where bisectors of angle R and angle S meet at point T

We know in quadrilateral, ∠ P + ∠Q + ∠R + ∠S = 360° ∠P + ∠Q = 180° -------------(1) ∠R + ∠S = 180° ( Angles on one common line makes 180°) In ∆RTS , ∠RTS + ∠TSR + ∠SRT = 180° --------------- (2) ∠TSR + ∠SRT â€‹ = 90° (These angle form by bisectors on ∠R and ∠S and we know ∠R + ∠S = 180° â€‹) Substitute this in equation (2) , we get ∠RTS + 90° = 180° ⇒∠RTS = 90° Multiply by 2 on both side , we get ⇒ 2∠RTS = 180° After substitute in equation (1) we get ∠P + ∠Q = 2∠RTSâ€‹ (Hence proved)

in a quadrilateral pqrs ,the bisectors of angle R and angle S meet at point T. Prove that angle P+ angle Q= 2angle RTS

in a quadrilateral pqrs ,the bisectors of angle R and angle S meet at point T.

Prove that angle P+ angle Q= 2angle RTS