Question

lines p q and r s are cut by a transversal a b if angle p and b is 55 degrees and angle r m a is 125 degrees prove that line p q and r s are pararrel​

Answer 1

Step-by-step explanation:

In PRT

In PRTBy angle sum property of triangle

In PRTBy angle sum property of triangle∠PRT+∠RPT+∠PTR=180 ∘⇒90 ∘ +45 ∘ +∠PTR=180 ∘⇒135 ∘ +∠PTR=180 ∘⇒∠PTR=180 ∘ −135 ∘⇒∠PTR=45 ∘ .Also,

⇒∠PTR=45 ∘ .Also,∠STQ=∠PTR

⇒∠PTR=45 ∘ .Also,∠STQ=∠PTR∠STQ=45 ∘ (vertically opposite angles)

⇒∠PTR=45 ∘ .Also,∠STQ=∠PTR∠STQ=45 ∘ (vertically opposite angles)In ΔSQT

⇒∠PTR=45 ∘ .Also,∠STQ=∠PTR∠STQ=45 ∘ (vertically opposite angles)In ΔSQTBy angle sum property of triangle

⇒∠PTR=45 ∘ .Also,∠STQ=∠PTR∠STQ=45 ∘ (vertically opposite angles)In ΔSQTBy angle sum property of triangle ∠SQT+∠STQ+∠TSQ=180 ∘

⇒∠PTR=45 ∘ .Also,∠STQ=∠PTR∠STQ=45 ∘ (vertically opposite angles)In ΔSQTBy angle sum property of triangle ∠SQT+∠STQ+∠TSQ=180 ∘∠SQT+75 ∘ +45 ∘ =180 ∘∠SQT+120 ∘

∠SQT+120 ∘=180 °∠SQT=180 ∘−120 ∘

∠SQT=180 ∘−120 ∘ ∠SQT=60 ∘