In the isosceles triangle PQR, the vertical angle $∠ P = 50 °$ . The circle passing through Q and R cuts PQ in S and PR in T. ST is joined. Find $∠ PST$

Question

In the isosceles triangle PQR, the vertical angle ∠ P = 50
° The circle passing through Q and R cuts PQ in S and PR in T
ST is joined Find ∠ PST

Global Expert · Accepted Answer

∠PQR=∠PRQ         (∵PQ=PR)In ∆PQR, we have:∠PQR+∠PRQ+∠QPR=180°  (Angle sum property)⇒2∠PRQ=180°-50°⇒∠PRQ=65°∠PRQ+∠QST=180° (STRQ is a cylic quadrilateral)⇒∠QST=180°-65°=115°∠PST+∠QST=180°   (Linnear pair)⇒∠PST=180°-115°=65°

In the isosceles triangle PQR, the vertical angle ∠ P = 50 ° . The circle passing through Q and R cuts PQ in S and PR in T. ST is joined. Find ∠ PST

In the isosceles triangle PQR, the vertical angle $∠ P = 50 °$ . The circle passing through Q and R cuts PQ in S and PR in T. ST is joined. Find $∠ PST$