Question

Find the size of unknown angles

Answer 1

Answer:

Step-by-step explanation:

2∠0PQ = 36

∠OPQ = 36/2 = 18°

Join OQ,

ΔOPQ is an isosceles triangle as OP = OQ = radius

∠OQP = ∠OPQ    {Angles opposite to equal sides are equal}

∠OQP = 18°

∠ORQ = 36

ΔORQ is an isosceles triangle as OR = OQ = radius

∠OQR =   ∠ORQ    {Angles opposite to equal sides are equal}

∠OQR = 36°

∠PQR = ∠PQO + ∠OQR

          = 18 + 36

∠PQR = 54°

∠POR = 2*∠PQR         {Central angle theorem}

          = 2 * 54

∠POR = 108°

∠PQR + ∠PSR = 180      {Opposite angles of cyclic quadrilateral}

54 + ∠ PSR = 180

            ∠PSR = 180 - 54

∠PSR = 126°

∠PSR + ∠RST = 180        {linear pair}

126 + ∠RST = 180

      ∠RST = 180 - 126

      ∠RST = 54°

Answer 2

Step-by-step explanation:

Hope it is helpful for you

thank you